Thursday, 19 June 2014 15:51

H1-27: SPEED OF SOUND - LISSAJOUS FIGURES

• ID Code: H1-27
• Purpose: Measurement of the speed of sound in air using Lissajous figures.
• Description: The signal to the loudspeaker is used as the horizontal input of an oscilloscope, and the signal picked up by the microphone is used as the vertical input, forming Lissajous figures. When they are in phase a diagonal line is produced, running from the lower left to the upper right of the oscilloscope screen. This situation is seen in the photograph above.

As the microphone is moved away from the loudspeaker the vertical signal falls 90 degrees behind in phase, causing the Lissajous figure to form an ellipse. When the two signals are out of phase (180 degrees phase difference) the pattern is a line along the opposite diagonal. As the microphone is withdrawn further, the microphone signal becomes 270 degrees behind in phase and the pattern again becomes an ellipse. One important difference between the two ellipses is that they are rotating in opposite directions, but this is not observable on the oscilloscope. Withdrawal of one full wavelength, when the signal from the microphone lags a full period (360 degrees) behind the original condition, creates a pattern similar to the original pattern. In this case the signal picked up by the microphone is reduced in amplitude due to the inverse square law, reducing the slope of the line.

For the most accurate measurement a frequency meter is connected to the trigger output of the oscillator. In the case shown below:

S = 3385Hz x 104mm = 352 m/s.

The photographs above show the Lissajous patterns at 90 degree intervals as the microphone is withdrawn.

• Availability: Available
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