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Oscillations

  • H4-12: LISSAJOUS FREQUENCY MEASUREMENT

    H4-12
    Show how frequencies can be matched using Lissajous figures.
    Obtain a Lissajous figure using a sine wave oscillator (on the horizontal axis) and a musical sound such as a voice or instrument (on the vertical axis). In the photograph above, a soft falsetto voice (approximately a sine wave) was used on the vertical axis to produce the Lissajous figure, then grabbed by the scope for a stable display. The frequency of the oscillator is displayed at the upper right of the oscilloscope tube. Using the Lissajous figure and the frequency of the oscillator the frequency of the musical note can be determined.
    H4, ME2, ME3

  • H4-14: LISSAJOUS FIGURES - VOICE

    H4-14
    Provide a Lissajous type display from a single vocal source.
    The signal from a microphone is amplified and fed into a circuit which produces two signals which are different in phase, and these two signals are fed into the X and Y coordinates of the oscilloscope to create a type of Lissajous pattern. The circuit makes the two signals exactly 90 degrees apart at 300 Hz, producing a circle. For other frequencies the phase shift is different and various figures are formed.
    H4, ME2, ME3

  • H4-18: LISSAJOUS FIGURES WITH SOUND

    H4-18
    Demonstrate the relation between "consonance" (musical intervals) and frequency ratios.
    Two identical oscillator/loudspeaker setups are sounded and simultaneously input into the two axes of an oscilloscope to produce a Lissajous figure. Two pitches which are related by simple rational whole numbers such as 3:2 or 5:4 are musical intervals and produce stationary figures. Beats between two close frequencies are also visibly evident by this technique. Try two close frequencies and two related by a small whole number interval for contrast. Let your students judge their consonance.
    H4, ME2, ME3

  • O4-13: FEEDBACK PATTERNS WITH B&W TV CAMERA AND MONITOR

    O4-13
    Demonstrate positive feedback in an amusing way.

    By pointing a black and white TV camera at a black and white TV monitor random positive feedback of the signals can be obtained. If the camera is rotated by 360/N degrees, where N is a small integer (say 3 to 6), pulsating or throbbing patterns with N-fold symmetry are produced.

    Tilt the camera at some angle. Using a pointer or your finger, adjust the height of the camera until it is even with the center of the screen. Focus on the pointer tip and move the camera along the optical axis until the magnification is one. The tilt of the camera produces the symmetry; slight changes produce various clockwise or counterclockwise motions.

    For this photo, the angle is 60 degrees, and the camera is at f2 about 1.5 meters from the monitor. Play around with the camera and TV controls until you get an interesting pattern. Then try to explain it.