Our pendulum wave demonstrations (G1-82 and G1-83) are popular ways of showing wave phenomena. These demonstrations consist of a series of pendulums in a line, each with incrementally different periods. They are all started into motion at once, so their first swing is in phase, but then they move out of synchronization due to their slightly different periods. The differences in period were chosen such that the array of pendulums would themselves describe a wave, with a period related to the difference in periods of the pendulums. So over time they evolve a series of wave patterns as different pendulums move in and out of synchronization, before eventually briefly synching up again when they finally reach an integral multiple of all of their periods.

 In a simulation, we can go beyond this, as removing the need for physical strings can enable even more complex wave patterns. Check out Don's latest animation below!

One popular demonstration in our collection for introducing concepts of wave optics is M1-11: Laser Interference: Fixed Double Slits.

Collimated light waves come from the laser and pass through a pair of narrow slits in the slide; the light passes through and then projects on the distant screen. But light travels as an electromagnetic wave, so when the light comes out of the two slits, it forms two wavefronts, just like ripples from two stones dropped in a pond. These two wavefronts can interfere with each other, as we can model with this pair of overlapping concentric circles. Where two peaks or two valleys of the wave pattern line up, they add together, interfering constructively; when a peak and a valley overlap, they cancel out, interfering destructively. The same happens with light waves; the light from the two slits overlaps, and creates a pattern of bright spots (constructive interference) and dark spots (destructive interference).

When using this in class, we can adjust the slide to use different sets of slits, with different slit widths and different spacing between the slits. This is a good opportunity to challenge students to predict how changing these two variables will change the resulting interference pattern.

 The spacing between the bright and dark fringes ultimately depends on three things: the distance between the slits and the screen, the wavelength of the light, and the spacing between the two slits. The first is probably obvious from your everyday experience – if you step farther away from the point that light spreads out from, it spreads out more!

 Likewise, if you increase the wavelength, the space between the peaks of the waves gets larger, so it’s not a surprise that the spaces between their overlaps would get bigger, too. The effect of the slit spacing, though, takes a moment to think about. If the slits move closer together, the two wavefronts are more and more similar; so the differences between them, the points where they fully cancel out, are farther apart. So increasing the slit spacing decreases the spacing of the fringes, and decreasing the slit spacing increases the spacing of the fringes.

We can see this modeled in a ripple tank simulation here in the Physlet Physics collection at AAPT’s compadre.org: https://www.compadre.org/Physlets/optics/prob37_7.cfm Use your mouse to measure the positions of the peaks relative to the double slit at the base of the image.

To experiment with this at home, check out this PhET Simulation at the University of Colorado: https://phet.colorado.edu/sims/cheerpj/quantum-wave-interference/latest/quantum-wave-interference.html 

 Use the button on the right of the simulation screen to activate the double slit barrier. You will then be able to simulate precisely this experiment!

Light of a particular frequency is released from a source, passes through a double slit, and then is projected on a virtual “screen.” So you can see both the interference pattern as it is formed through space, and the final pattern that you can detect at a distance.

Carrying out the computations for this simulation is processor intensive, so it may run slowly; and as you can see in the image, the resolution is limited. There are limits to how well software can simulate reality!

But at the same time, we can use the simulator to try things we can’t easily do in the laboratory. The slider at the bottom will let you change the laser’s frequency, variable along the full visible spectrum and a bit beyond (fun challenge: is there anything remarkable about the spectrum selection here?).

The sliders at the right will let you change some of the physical parameters of the barrier. You can modify the width of the slits, or the separation distance between the two slits. The “Vertical position” slider lets you adjust the distance between the slits and the screen.

So here we can see the value of combining both real-world experiments and simulations – each alone is useful in learning, and each has its benefits and limitations, but the combination lets us see things we cannot with either one or the other on its own.

This week we’re exploring the physics of polarized light! We have several demonstrations of polarization in our collection; two of the most popular are perhaps the most straightforward: M7-03, which consists of two polarizing filters (or polarizers) and a light source; and M7-07, which adds a third polarizer.

Light is an electromagnetic wave, made up of oscillating electric and magnetic fields. We call a wave polarized when this oscillation has a particular orientation as the wave travels through space. The direction of the electric field defines the direction of polarization of the wave.

You can see two polarizers in action in this video starring Prof. Manuel Franco Sevilla.

A polarizer like this, also called a polarizing filter, passes only light of a given linear polarization. So it acts as a filter; if the first one is polarized vertically, it will block any horizontally polarized component of the light, and pass only the vertically polarized components. When the two polarizers are in line (which is to say that their axes of polarization are aligned), the second polarizer has very little effect on the light passing through. The first polarizer creates linearly polarized light; the second one, with the same polarization, passes nearly all the light that came through the first one. If we rotate the second polarizer, though, the axis of polarization, the direction in which it requires light to be polarized in order to pass through, rotates. So when the second polarizer is out of line with the first polarizer, it is only passing whatever component of the light from the first polarizer is also in line with the second one. As they rotate farther apart, that component is reduced. Once the two polarizers are fully 90 degrees apart, they no longer have any component in common, so together they pass no light at all! If the first one is polarized entirely vertically, and the second is polarized entirely horizontally, they are perpendicular.

Which is an important aspect of physics that this demo shows: that linearly polarized light can be treated as having separable components, just like we can separate the component vectors of linear motion of an object in space, and a polarizing filter passes only light components parallel to its polarization. So if we add a third polarizer, canted with respect to the other two, it can pass components parallel to its axis of polarization, however we choose to orient that. This can have some interesting results, as we see in the next video, starring Dan Horstman.

 The passage of light depends on the orientation of the current wave’s polarization and the filter it encounters – so adding the third filter actually could allow more light to pass!

.Welcome back! This week, we’re looking at one of our particularly popular and versatile demonstrations, the Ripple Tank.

 The Physics Demonstration Facility has two versions of this demo, so we can reach as many audiences as possible. We have a table top version for outreach events and local classrooms, and a portable version to reach out-of-building locations. These ripple tank demonstrations can both be used to highlight a variety of wave phenomena.

A properly set up ripple tank with its various accessories, can illustrate many different aspects of the physics of waves – single and double point source circular waves, plane waves, interference, diffraction through openings and around obstacles. With a movable mount and careful planning, it can even show the Doppler effect!

Some of this is hard to do at home, but fortunately, there are options. Simulators exist that can carry out at least some of the experiments you might usually use the ripple tank for. You can take screenshots of them to illustrate lectures, or send the link to students to experiment with at home.

There are several different ripple tank simulators, such as this versatile one from Paul Falstad: http://www.falstad.com/ripple/ 

• When first opened, the simulator defaults to emulating a tank of water with a single oscillating source in it. It is tinted a cerulean color for easy viewing, but can be switched to several different color schemes via a drop-down menu. If you prefer the traditional view, #4 on that menu is a greyscale view that closely approximates the familiar shadow projection of the tabletop ripple tank.

• A checkbox below this allows the simulation to be frozen and restarted; another lets you shift to an angled three-dimensional view that can be more difficult to see on small screens, but can be helpful in clarifying complex wave behaviour.

• Sliders adjacent to this let you vary the frequency of the oscillation, and turn on damping.

• Other sliders let you adjust aspects of the simulation process, changing the speed, brightness, and resolution of the simulation box; these are best left alone unless you are struggling with making it work on a slower computer or are having difficulty clarifying complex wave behaviour at an interface.

• In addition to the preprogrammed oscillators, you can excite the simulated ripple tank manually by clicking on it, just like dipping your finger into the water of a real ripple tank.

• A variety of oscillation sources and tank configurations can be selected from the Example dropdown menu. Some likely to be useful for our purposes include:

1. Single Source and Double Source for circular waves from point sources

2. Plane Wave (which does show edge effects at the sides of the “tank”)

3. Single Slit and Double Slit which show diffraction via a plane wave striking a barrier with one or two holes and producing the expected circular waves and interference pattern

4. Obstacle (with a single source circular wave and a small rectangular barrier)

5. Doppler Effect 1 (with a moving source of circular waves).

• For more complex uses, you can also modify the simulation. By right-clicking in the simulation box, you can place additional sources, barriers, and refracting elements. You can also right-click on existing elements and delete them, allowing you to clear the screen and produce an empty “tank” to create your own experiment in.

• You can also place “probes” that will display the wave pattern at that point in a movable oscilloscope-style box. This can be valuable as a challenge for students, to predict the pattern that a probe would read at a given point, or to construct a simulation to produce a particular result.

Today, let’s take look at a popular multi-function demonstration apparatus: The Shive Wave Machine. You can see it in action in this new video featuring Prof. Peter Shawhan.

 Invented in 1959 by Dr. John Shive, a Baltimore native who became a physicist at Bell Labs, the Shive Wave Machine consists of a series of heavy steel rods connected at their centers by a stiff wire; it functions like a torsional spring. You can create a pulse by gently moving the rod at one end up and down; then you can see how the pulse propagates as a wave along the length of the wire, watching each rod move in turn. Our demonstration collection has two such devices; one has longer rods, the other has shorter rods; as you can see in the video, the different weights thus give them different transmission speeds and impedances.

This can be used to demonstrate a variety of wave phenomena. You can make a simple model of a traveling wave by first sending a single pulse down the length of the apparatus. The torsion wire in the center transmits energy from one rod to the next. As in all mechanical waves, the individual components that make up the wave, whether they be rods on a wire or molecules in air or water, do not travel far from their starting points; what travels from the beginning to end is not the particles or other elements, but the energy of the wave and the pattern of disturbance it creates. The disturbance moves down the line, but the rods return to their starting points. No matter how large or small the pulse, it travels at the same speed within a given medium, determined by the impedance. If we create the same pulse on the other unit, with a different impedance, the wave travels at a different speed.

Similarly, you can model superposition of waves by sending pulses from both ends simultaneously. We can see that the two pulses pass through one another without interacting. At the point where they cross, the pulses may superimpose additively or subtractively, depending on whether they are in phase or out of phase, but they then each move on in their original directions.

When we send a pulse down the length of the device and it reaches the far end, the pulse reflects off the open end and returns to where it started, looking much like it did when it was going the other way.

But if we clamp the far end in place so that the last rod is fixed in place, then when we send the same pulse down the length of the device and it reaches the end, it still reflects back – but inverted! The pulse is upside-down from its original orientation. Whether reflection from an end is upright or inverted depends on whether the end is open and free to move, or closed and fixed. If instead we clamp the two Shive devices with different impedances together, we can see a partial reflection – part of the pulse reflects back and part of it passes on into the second medium. How much reflects and how much passes through depends on the difference in impedance. The reflection from an open or fixed end is essentially the extreme case of this – in a sense, it’s reflecting back all of the energy from something with effectively zero or infinite impedance.

You can see Prof. Shawhan put the Shive apparatus through its paces in the video above! To explore this device some more, try out this simulator [click here for simulator]. This simulator replicates some of the behaviours of the Shive wave machine. The dropdown menu at the top lets to adjust the configuration, and the Play button can initiate a pulse.

Also, you can make a simple one at home! The Science House at North Carolina State University has published plans for making your own simple wave machine from household items. Check them out in pdf form here: https://sciencehouse.ncsu.edu/wp-content/uploads/2017/03/Soda-Straw-Torsional-Waves-Oscillations.pdf and visit their site for other fun remote learning ideas!

Some Shive Wave Machine demonstrations in our collection

•  G3-01: Traveling Waves
•  G3-02: Superposition of Pulses
•  G3-03: Reflection of Pulses
•  G3-04: Standing Waves
•  G3-05: Partial Reflections
•  G3-06: Impedance Matching
•  G3-07: Tapered Transformer

The Flame Tube, or Rubens Tube, is a classic device for showing the wave structure of sound. It was named for German physicist Heinrich Rubens, who developed it around the turn of the last century.

 You can see our own flame tube demonstration in action in this video starring Prof. Norbert Linke

The device is, in essence, and oscilloscope without the electronics – it transforms a sound wave into a visible trace by allowing the changes in pressure in the gas in the tube to drive flames to different heights along the top. In this way, you can see that sound does form a wave, and can show a standing wave and measure its wavelength.

 To learn more about the Rubens’ Tube, explore these links:

• Flame Tube at UMD Lecture-Demonstration

• Rubens’ Tube at Wikipedia

• The Flaming Oscilloscope: The Physics of Rubens' Flame Tube by Tamela Maciel at Physics Buzz

• Chemistry Experiments with the Flame Tube by Tom Kuntzelman at Chem Ed Xchange

Joseph Fourier and the Fourier Transform

Joseph Fourier was a French scientist in the late 18^th and early 19^th centuries. He made important contributions to subjects ranging from algebra to thermodynamics, including early studies on the greenhouse effect on Earth’s climate, but today is best remembered for his discovery that many mathematical functions can be approximated more simply as a sum of basic trigonometric functions (sines and cosines).

 This process is particularly useful to us because of the realization that you can analyze the structure of any waveform by breaking it down into a series of sine waves. By doing this, we can represent the wave as a list of simple sines and cosines, and their relative amplitudes and phases. We can build up a complex waveform by taking a single sine wave, then adding harmonics of it (sine waves whose frequency is an integral multiple of the fundamental sine wave) in different amplitudes and different phases.

 We can then work with these sine and cosine waves mathematically in order to manipulate the original waveform. This is used in modern technology for many things, from audio equalizers on music players, to cleaning up errors in digital photographs, to analyzing the complex interference patterns from spectroscopy and crystallography used to identify substances in the laboratory.

 This all sounds very complex; but the fundamentals of it are quite simple, and you can try it for yourself!

 Each of these pairs of images represents a single waveform. In the first picture, we see the full wave. In the second, we see the Fourier Transform of that wave – the spread of sine waves of different frequencies that can be assembled to build that waveform. Each spike in the Fourier Transform graph represents a sine wave; the height of each spike is how large the amplitude of that sine wave should be to make the full wave.

When the waveform we put in is just a sine wave itself, of course the Fourier Transform of it is a single line – it’s just that same sine wave again!

This more complicated sawtooth wave is made up of many Fourier components – multiple sine waves. As the frequency goes up, the amplitude goes down.

Each of these sine waves is a harmonic of the first one; the frequency of each is two, or three, or four, etc times the frequency of the first, or fundamental, sine wave. That fundamentalhas the same frequency as the original sawtooth wave.

These graphs were all created with an oscilloscope and waveform generator in our facility; check one out here!

Match the Wave!

Now try it for yourself! Here are some more waveforms:

and some Fourier transforms. Can you guess which Fourier transform came from which wave?

Make Your Own Waves

Even without a complex electronic synthesizer, you can try this at home with a simulator.

This interactive simulatorin the PhET collection lets you build up waveforms by adding Fourier components: https://phet.colorado.edu/en/simulation/legacy/fourier

And the Falstad collection has another interactive simulator to discover the Fourier components of many different wave forms, and see how the breakdown of components changes when the wave does. You can also turn on the sound generator and compare how different waveforms sound to your ear. Try it out, and see what you can change in a wave to change what you hear – and what you can change and have the wave still sound the same. Can you hear a chance in frequency? A change in phase? http://www.falstad.com/fourier/

Try out both, and see what waves you can build and explore!

Welcome back! In this entry in our Demonstration Highlights series, we’re taking a look at Fourier Synthesis. You may recall that we addressed Fourier Analysis in a previous entry, the process of analyzing a waveform by breaking it down into harmonic components. This time, we’re taking the process in reverse. In Fourier Synthesis, we assemble a wave form by adding sine waves together.

Our Fourier Synthesizer demonstration, H4-01 in the demonstration index, lets you generate a sine wave of any frequency between 100Hz and 1,000Hz. The synthesizer then generates harmonics of this frequency, waves with integer multiple frequencies – e.g. 120Hz, 240Hz, 480Hz, etc. You can then choose to add any or all of these harmonics to the output of the synthesizer. For each of these harmonics, you can then adjust two variables: the amplitude of the harmonic, and its phase (whether it is in synch or out of synch with the original waveform).

 As Joseph Fourier showed us last time, you can create approximations of any other wave by assembling harmonics in this way.

You can try this at home with the updated Making Waves simulation in the PhET Collection at the University of Colorado. This simulator works much the same way as our demonstration, allowing you to select the amplitude of each harmonic, and display them both individually and in sum. Try it here: https://phet.colorado.edu/en/simulations/fourier-making-waves

In the top third of the screen, you set the amplitude of each harmonic. The middle third shows graphs of each harmonic, and the bottom third shows the sum of all of them. Try building a square wave, or a sawtooth wave, and see how close you can get!

Our Guitar and Oscilloscope demonstration is a fun hands-on way to show a visualization of a waveform while students also hear it. It illustrates how waves on a string become sound waves in air, and how the decay times of different components of a complex waveform affect its sound over time. You can see it in action in our new demonstration video, starring physics student Alana Dixon.

A guitar produces sound from the vibration of the strings. When you strum or pluck a string, the string vibrates. The frequency of this vibration is determined by the string’s length, its tension, and its weight. The body of the guitar, and the air chamber within, can couple and resonate with these vibrations. The energy therein is passed to the air, creating the sound waves we hear across the room. A pickup has been attached to the guitar; this pickup uses magnetic induction with the strings to detect the vibrations and transform them into an electrical signal. This is then amplified by the amplifier and displayed by the oscilloscope. An oscilloscope displays a changing electrical voltage as a moving point on a graph. It allows us to display visually how the signal changes over time.

When we pluck a string, we can see the resulting sound wave reflected as a waveform trace on the oscilloscope. There is a slight difference, though: the pickup is showing the vibrations from the string, and the vibration of the body as well since it is connected to the body, but this is not always exactly identical to the wave as transmitted through the air! The particular shape of the guitar body and sound hole can emphasize slightly different elements of the sound as they couple with the outside air. But for the purposes of our experiments, it’s close enough.

 The frequency produced by a vibrating string is determined by three factors: the length of the string, the tension in the string, and the linear density of the string. These define boundary conditions for the waveforms. Guitar strings have different linear densities (the weight per unit length) to help them produce a wider range of sounds. Then we adjust the tension in each string to tune the guitar to the exact frequencies we want. You’ll notice, though, that the waveforms we see here are not simple sine waves. The sound of a guitar is a very complex waveform that changes over time. The complexity of the waveform is in part due to the design of the instrument. There are several modes of coupling within the guitar, as energy passes from the vibrating strings to the surface of the guitar (the soundboard), from there to the air inside the body, and between the body and the outside air. And the complex shape of the instrument creates multiple possible resonances at various frequencies. All of these can reinforce certain harmonics of the fundamental wave, and these components add up to form the complex waveform we see on the oscilloscope screen. Additionally, the different components of the wave last different amounts of time. After the string is plucked, its vibration slowly dies down, but the vibrations it has set up within the instrument also last for different amounts of time – each component has its own decay time. As these components change in amplitude, the shape of the overall waveform changes, and that gives the guitar its complex sound and varying sound.

To understand this better, we can examine some simulations of how a string responds to being plucked, and its behaviour over time.

This simulation from Falstad http://www.falstad.com/loadedstring/ lets you pluck a string and see how the resulting wave in the string gradually decays. It will display graphs of both the amplitude and phases of various harmonics that make up the wave. Try adjusting the damping to see how that changes the decay over time!

If you’d like to learn more, check out this breakdown https://www.acs.psu.edu/drussell/Demos/Pluck-Fourier/Pluck-Fourier.html  by Dr. Daniel Russell of Penn State with both graphical and mathematical treatments of the initial conditions of a plucked string and its evolution over time.

Further Reading:

 Fred W. Inman. A Standing-Wave Experiment with a Guitar

The Physics Teacher 44, 465 (2006); https://doi.org/10.1119/1.2353595

Michael C. LoPresto. Experimenting with Guitar Strings

The Physics Teacher 44, 509 (2006); https://doi.org/10.1119/1.2362942

Polievkt Perov, Walter Johnson and Nataliia Perova-Mello. The physics of guitar string vibrations

American Journal of Physics 84, 38 (2016); https://doi.org/10.1119/1.4935088

Michael Sobel. Teaching Resonance and Harmonics with Guitar and Piano

The Physics Teacher 52, 80 (2014); https://doi.org/10.1119/1.4862108

Scott B. Whitfield and Kurt B. Flesch. An experimental analysis of a vibrating guitar string using high-speed photography

American Journal of Physics 82, 102 (2014); https://doi.org/10.1119/1.4832195

Welcome back to the Demonstration Highlight of the Week! This week, we’re taking a look at G1-31: Hooke’s Law and Simple Harmonic Motion. You can see it in action in this video starring PhD student Subhayan Sahu.

 In this demonstration, we have a spring that is reasonably well described by Hooke’s Law – that is, within its usual range the spring responds linearly to force. We hang a series of 200 gram masses from the spring, and by measuring the displacement and the period of oscillation we can determine the spring constant, k.

 You can try this kind of experiment at home as well! If you don’t happen to have a spring handy, the PhET Collection has a simulated one you can use: https://phet.colorado.edu/en/simulation/masses-and-springs .

 This demonstration is an excellent example of how we can use multiple measurements in scientific experiments. The value of k (or, of kis known, of g) can be determined from the displacement, or from the period of oscillation. By measuring both, we can test our assumptions about the system.

Welcome back! Physics PhD student Subhayan Sahu returns this week for another installment in our series highlighting oscillation demonstrations. This week’s highlight: Demonstration G1-14 Pendula With Different Masses. Check out his video below:

These swinging cubes are made of a variety of materials, from aluminum to lead. We can see that for a simple pendulum swinging under gravity, the period is dependent only on the length. So long as these pendula all have the same length, they have the same period!

You can try this for yourself in the PhET Collection’s Pendulum Lab simulation. In the lab, create two pendula with the same length and mass. Pause the simulation while you position them to the same height and release; you’ll see they have the same period. Now reduce the mass of one while keeping the mass of the other fixed; the period stays the same! Now try changing the length of one pendulum to see how that changes the period.

Today we’re looking at two demonstrations that are often used, individually or together, to discuss simple harmonic motion. Demonstration G1-11: Comparison of Simple Harmonic Motion and Uniform Circular Motion, is a simple mechanical model with a large rotating arm with a disc mounted on it. As the arm-mounted disc rotates around the center, we can see that its motion describes a circle in space. The arm is linked mechanically to a second disc mounted above, that slides back and forth as the arm rotates. The upper disc keeps pace with the lower disc, and as the arm rotates, the upper disc moves back and forth as though it were mounted on a spring.

Demonstration G1-12: Pendulum and Rotating Ball, lets us see that this is not just a coincidence of the model. A ball is mounted as the bob on a rigid pendulum, while an identical ball is mounted on a rotating platform below. The rotating platform is motorized so that it will spin at a constant speed; the pendulum is of an appropriate length so that the period of the swing is the same as the rotational period of the platform. If you start them moving from the same point at the same time, then you can see that the two balls move in sync. By positioning a bright light in front of the apparatus we can project the shadows of both balls on the wall behind, and we can see that the two balls are executing nearly the same motion.

A ball executing simple harmonic motion – the motion of a pendulum bob – is equivalent to the projection of a ball executing uniform circular motion. This is not just a coincidence of the apparatus, but a fundamental discovery about the mathematics behind repeating motion.

(diagram based on public domain work by Wikimedia user Yohai)

 If we make a graph of the linear position of a point on the rotating disc as a function of time, that graph traces out a repeating curve – a curve we can describe with the cosine function, Acos(ɷt),where A is the radius from the center of the circle to the point andt is time. For those of you who have studied thebehaviour of harmonic oscillators, that function should look familiar – it’s the same way we describe an object oscillating without damping, what’s called simple harmonic motion.ɷ(omega) isthe rate of rotation of the disc, and equivalent tothe angular frequency of the oscillation. And conversely, if you made a graph of the velocity of an oscillating mass against its position,rather than plotting the position or the velocity against time,that graph would also trace out a circle. It’s not just a coincidence, but reality – rotational motion and oscillating motion are fundamentally the same phenomenon from a mathematical perspective, just looked at in different dimensions.

 (PD Animation credits: Wikimedia users Chetvorno & Mazemaster)

Let's try this at home. This simulator, by Andrew Duffy of Boston University, lets us model this behaviour on the screen, and see what happens when we change parameters of the motion. Check it out at http://physics.bu.edu/~duffy/HTML5/SHM_circular_motion.html .

 This simulator lets us view this motion in real time. Press Play and see a point rotating on the disc, while two more masses oscillate on springs vertically and horizontally next to the disc. The graph plots out the vertical motion of both the point on the disc and the vertical oscillator over time. You can click the checkbox at the bottom of the screen to form virtual lines between the masses, to show they’re in sync.

Now try changing the experiment. There are two sliders at the bottom of the simulation. The slider on your left lets you change ɷ –try speeding it up and watch what happens! The slider on your right lets you change the radius of the disc, and thus the amplitude of the oscillation.

 Try it out for yourself! And think about where else you’ve seen graphs like that. There are many other physical phenomena that obey similar mathematics, including all types of waves. What examples can you think of?

An important concept in physics is simple harmonic motion – the periodic motion of a mass with a restoring force proportinal to its displacement. This force might come from gravity, a spring, or many other sources, but the same mathematics describes their motion. We have many demonstrations of simple harmonic motion (or SHM) in our collection, including G1-01 and G1-52, which you can see in action in this video starring UMD PhD student Subhayan Sayu.

You can experiment with this at home! Any mass on a spring or on a string or rolling in a well can be a pendulum. Or, try out these Periodic Motion simulations at the PhET Collection: Pendulum Lab or Masses and Springs.

The University of Cambridge offers an example of a simple pendulum experiment to try at home; check it out at https://nrich.maths.org/5376

Demonstration J4-51: The Theremin is a fun and exciting way to illustrate electrical capacitance. You can see it in action in this new video with Angel Torres.

The theremin is an electronic musical instrument invented in the early 20^th century by Russian scientist, engineer, and cellist Leon Theremin. As well as his musical work, Leon Theremin developed many other electronic devices in his career as an engineer, including an early motion detector and listening devices for espionage.

The two metal “antennas” on the sides of the theremin are not antennas in the usual sense. Each one functions as one plate of a capacitor. When you move your hand near the antenna, your hand serves as the other plate of that capacitor. Thus, each functions as a variable capacitor, where the capacitance, the ability of this air-filled capacitor to store electrical charge, varies as you move your hand and body near the antenna.

Each of these capacitors is part of a variable RLC (resistor-inductor-capacitor) oscillator circuit. One of these variable oscillators controls a second internal oscillator circuit; these together create the output frequency (or pitch) of the sound from the theremin.

The other variable oscillator, meanwhile controls the output amplitude. The resulting signal is fed through an amplifier circuit to a speaker. Together they form an electronic system that can create music, controlled by the motions of your body – without the player ever actually touching the device.

The theremin has been used in a wide range of music. Much of the early technique of playing it was developed by classical violinist and thereminist Clara Rockmore. The theremin can be heard in the work of orchestral composers like Dmitri Shostakovich and Percy Grainger, and in rock bands including the Rolling Stones and Led Zeppelin. And you can hear it on the sound tracks of movies ranging from Cecil B. deMille’s The TenCommandments, to the science fiction classic The Day the Earth Stood Still, to the 2006 animated film Monster House.  It’s a beautiful way to see and hear the fusion of art and science.

Our theremin seen here was built by the Moog Corporation, best known for their electronic synthesizers.

Read More:

• Theremin World http://www.thereminworld.com/
• Theremin Times https://theremintimes.ru/en/
• Moog Theremins https://www.moogmusic.com/synthesizers?type=52
• Articles in the American Journal of Physics
• -The Physics of the Theremin, Skeldon et al.: https://aapt.scitation.org/doi/abs/10.1119/1.19004
• -Theremin Oscillators and Oscillations, N. Holonyak: https://aapt.scitation.org/doi/abs/10.1119/1.19267

 Originally appearing in our demonstration catalog as J3-23 and now as the updated K8-46, the Faraday Cage and Radio Waves demonstration is a popular way of showing how a conductive surface interferes with the passage of electric fields, and thus can prevent the transmission of electromagnetic waves.

Now, our own Don Lynch has created an animation of the physics behind this demonstration; check it out below! 

 The Lecture-Demonstration Facility is introducing a series of teaching aid animations of popular demonstrations; watch for more coming soon!

UMD Faculty: Are you interested in showing wave phenomena in class, but unsure if the familiar lecture-hall sized Shive Wave Machine and Ripple Tank will fit in your seminar or discussion room? Here’s another demonstration you may want to check out! 

The new portable ripple tank is a small desktop-sized device we use in our physics classes here at the University of Maryland that produces waves in a small tabletop tank. It can be used hands-on for small groups to gather around in the classroom, or displayed on screen with a digital camera for larger audiences.

We fill a small tank with water, and illuminate it with the built-in LED strobe. A small stepper motor drives vibrating needles at the edge of the tank, generating ripple patterns that propagate through the tank. The strobe rate is adjustable, allowing you to seemingly slow down or freeze the movement of the waves to highlight particular interference effects, or you can switch it over to steady illumination to show wave propagation in real time.

Waves themselves are an important physical phenomenon regardless of medium. A demonstration like this shows how waves form in water as a result of a driving force, and are propagated through the water – but, interestingly, while the wave as a structure is moving across the tank, the water is not! At any given point, most of the water is only moving up and down in place, not across the tank. The wave is a physical phenomenon independent of the molecules making up the water. It carries energy across the tank, but mostly not the water itself.

With two sources of wave motion, we can see interference patterns form. Where the peak of one wave meets the peak of another, a larger wave is formed; where the peak of one wave meets the trough of another, they cancel out, forming an oddly calm spot amid the rippling surface. Two waves that line up with their peaks overlapping perfectly are in phase with each other; waves where the peak of one exactly matches the trough of another are out of phase.Where this kind of interference occurs repeatedly across the surface as wavefronts interact, in phase and out of phase at different points, an interference pattern is formed, as the individual waves interfere with each other.

Challenge your students to predict how the interference patterns will change as you vary the vibration rate!

A valuable trait of waves is that many of the properties of wave phenomena are the same for all waves, in any medium. Just like these waves of moving water, other waves light sound waves, radio, and light propagate through space, and can interfere and form interference patterns. The Ripple Tank is a good way to introduce these concepts in class in a familiar form, and analogues can then be drawn to how these effects appear in other situations. The way waves of water diffract around a barrier is much like the way sound waves diffract around a sound-baffling wall by the highway; the calm spots formed by two out of phase sources interfering are much like the quiet zone formed by noise-cancelling headphones as they repeat a soundwave with its phase inverted to remove background noise.

Try out a demo sometime and explore the word of wave physics. But don't get seasick!

UMD Physicists are heavily involved with the LIGO collaboration, the Laser Interferometer Gravitational-Wave Observatory that detects and analyzes gravitational waves to study distant celestial phenomena. Several recent papers have announced important new findings. One highlight is the observation of merging black holes including the largest one yet observed in such a merger.

 The merger of these massive objects distorts spacetime around it, creating a ripple that we can detect here on earth through the use of extremely precise interferometery. Some of you may recall presentations we hosted a few years ago when LIGO announced their first detections. New research from this team is coming in all the time!

 Read more about recent discoveries:

• Maryland Today: Heaviest Black Hole Merger Spotted

• CMNS: Heaviest Black Hole Merger is Among Three Recent Gravitational Wave Discoveries

• Physical Review Letters: R. Abbott et al. (2 Sept 2020). “GW190521: A Binary Black Hole Merger with a Total Mass of 150M⊙.”

• Astrophysical Journal Letters: R. Abbott et al. (2 Sept 2020). “Properties and Astrophysical Implications of the 150 M ⊙ Binary Black Hole Merger GW190521.”

• Upcoming in IOP’s Classical and Quantum Gravity: Sullivan et al. “Can we use next-generation gravitational wave detectors for terrestrial precision measurements of Shapiro delay?”

   

More places to visit:

• UMD Physics Gravitation Experiment Group
• UMD Physics Gravitation Theory Group
• LIGO Homepage

December’s issue of Physics Today has a special theme, celebrating the International Year of Sound. The cover features art from Ray Walker’s Hackney Peace Mural in London; topical articles range from acoustic reproduction in historical and cultural preservation, to acoustics in climate change research.

 Sponsored by the International Commission on Acoustics, the International Year of Sound is an education and outreach project to promote understanding of the science of sound and of acoustic best practices.

•  Read more about the International Year of Sound at https://sound2020.org/ .
•  Physics Today: https://physicstoday.scitation.org/toc/pto/73/12

‘Tis the spooky season, and what could be more seasonal than bats? This week we’re exploring a different kind of bats than the usual, though. So let’s take a swing at the physics of baseball and softball bats!

A baseball or softball bat is an irregularly shaped object that is swung as a lever and then experiences a large impact. This impact sets up vibrations in the bat; you can see several vibrational modes modeled on this webpage created by Dan Russell of Penn State University: https://www.acs.psu.edu/drussell/Demos/batvibes.html He illustrates here that wooden bats are solid, and bend lengthwise, like a tuning bar; aluminum and composite bats, however, are frequently hollow, and can flex across their diameters as well, like a hoop or bell.

One of the most widely recognized specialists in the field of baseball physics is Alan Nathan of the University of Illinois; you can check out his homepage here: http://baseball.physics.illinois.edu/ where he discusses many aspects of the physics of the sport, current and historical. Particularly interesting is his collection of slow-motion images of ball and bat collisions and their analysis: http://baseball.physics.illinois.edu/ball-bat.html .

 You can experiment with this physics yourself with our demonstration D2-21 Center of Percussion: Bat and Mallet. 

 Many articles have been published over the years exploring the physics of bats, particularly with a view to classroom discussion. We’ve collected for you some highlights from the American Journal of Physics and The Physics Teacher, presented chronologically so you can explore the development of this topic over time.

H. Brody. “The sweet spot of a baseball bat”

American Journal of Physics 54, 640 (1986); https://doi.org/10.1119/1.14854

Explores the idea of a bat’s “sweet spot,” the point of impact at which maximum energy is imparted to the ball.

G. Watts & S. Baroni. “Baseball–bat collisions and the resulting trajectories of spinning balls”

American Journal of Physics 57, 40 (1989); https://doi.org/10.1119/1.15864

Examines collisions between bat and ball as rigid bodies.

H. Brody. “Models of baseball bats”

American Journal of Physics 58, 756 (1990); https://doi.org/10.1119/1.16378

Examines collisions between bat and ball and the bat’s vibrations, treating it as a free object in space.

L. L. Van Zandt. “The dynamical theory of the baseball bat”

American Journal of Physics 60, 172 (1992); https://doi.org/10.1119/1.16939

Models the bat as a vibrating elastic mass with a normal mode.

R. Cross. “The sweet spot of a baseball bat”

American Journal of Physics 66, 772 (1998); https://doi.org/10.1119/1.19030

Compares the calculation of a bat’s “sweet spot” as the center of percussion or as a vibrational node.

A. Nathan. “Dynamics of the baseball–bat collision”

American Journal of Physics 68, 979 (2000); https://doi.org/10.1119/1.1286119

Presents a way to model the physics of the collision between a bat and a ball.

A. Nathan. “Characterizing the performance of baseball bats”

American Journal of Physics 71, 134 (2003); https://doi.org/10.1119/1.1522699

Introduces ways of measuring and modeling baseball bats in the physics lab.

R. Cross. “A double pendulum swing experiment: In search of a better bat”

American Journal of Physics 73, 330 (2005); https://doi.org/10.1119/1.1842729

Looks at the motion of a double pendulum and how it can model the swing of a bat or racquet.

R. Cross & A. Nathan. “Scattering of a baseball by a bat”

American Journal of Physics 74, 896 (2006); https://doi.org/10.1119/1.2209246

Examines the relationship between distance, speed, and spin of a ball hit by a bat.

R. Cross & A. Nathan. “Experimental study of the gear effect in ball collisions”

American Journal of Physics 75, 658 (2007); https://doi.org/10.1119/1.2713788

Looks at the possibility of whether slippage between surfaces in a baseball impact can be modeled like meshing gears.

R. Cross. “Mechanics of swinging a bat”

American Journal of Physics 77, 36 (2009); https://doi.org/10.1119/1.2983146

Models the force pairs at work in swinging a bat.

D. Russell. “Swing Weights of Baseball and Softball Bats”

The Physics Teacher 48, 471 (2010); https://doi.org/10.1119/1.3488193

Explores the moment of inertia of bats, commonly called the “swing weight” in sports writing.

A. Nathan, L. Smith, & D. Russel. “Corked bats, juiced balls, and humidors: The physics of cheating in baseball”

American Journal of Physics 79, 575 (2011); https://doi.org/10.1119/1.3554642

Examines the physics underlying several baseball controversies.

D. Kagan. “The vibrations in a rubber baseball bat”

The Physics Teacher 49, 588 (2011); https://doi.org/10.1119/1.3661118

Discusses some experiments with a rubber bat.

I. Aguilar & D. Kagan. “Breaking Bat”

The Physics Teacher 51, 80 (2013); https://doi.org/10.1119/1.4775523

Describes experiments with the breaking points of different wooden bats.

J. Kensrud, A. Nathan, & L. Smith. “Oblique collisions of baseballs and softballs with a bat”

American Journal of Physics 85, 503 (2017); https://doi.org/10.1119/1.4982793

Examines ball and bat collisions with a high speed camera.

K. Wagoner & D. Flanagan. “Baseball Physics: A New Mechanics Lab”

The Physics Teacher 56, 290 (2018); https://doi.org/10.1119/1.5033871

Describes a series of student lab activities to explore the mechanics of baseball.

And one final note, on balls rather than bats: new work in materials science is studying how softer materials inside solid projectiles can affect how they launch. Read all about it in this new post at the American Physical Society website:

Springy Material Boosts Projectile Performance https://physics.aps.org/articles/v13/160

 Update: And for those who read all the way to the end but are still upset about the lack of cute fuzzy bats: "What Bats Can Teach Humans About Coronavirus Immunity" at JSTOR Daily