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^o behind in phase, causing the Lissajous figure to form an ellipse. When the two signals are out of phase (180^o phase difference) the pattern is a line along the opposite diagonal. As the microphone is withdrawn further, the microphone signal becomes 270^o behind in phase and the pattern again becomes an ellipse.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^o) 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:

The photographs below show the Lissajous patterns at 90^o intervals as the microphone is withdrawn.

SUGGESTIONS:

See paper about this demonstration written by Berg and Brill. Here is a Proof Copy of the article in The Physics Teacher.

See Question of the Week #157 for information on using this demonstration to enhance class involvement.

REFERENCES: (PIRA unknown.)

EQUIPMENT: Oscilloscope, microphone and loudspeaker on optical supports, with frequency counter, as photographed.

SETUP TIME: 5 min.