# Experiment of the Month

# Sound Velocity

*The MU Physics Department does not claim to have invented these labs. Actually, the origin of these labs is currently unknown to us. Our labs do not have written instructions. In keeping with this spirit, the description given here will be brief and general. The intent is that each performance of the lab will be unique; in each nature will reveal a slightly different face to the observer.*

Students like to compare their laboratory results to see if they "got it right." We discourage comparison of results to the "book value," which leads to the idea that the experimental error is the difference between their answer and the book result.

When we measure the acceleration of a freely falling body, we do not compare the results to 9.8 m/sec^2: We measure it in two or three successive weeks, with different methods. In each exercise, we estimate the uncertainty in the result, using the variation in repeated measurements. Finally, we compare the three results, asking if they agree within the limits of uncertainty.

When we measure the speed of sound, we do it with two different methods, and ask if the results agree within uncertainty limits.

We measure the group velocity by measuring the time it takes a hand-clap sound to travel a measured distance. Following a suggestion in Crawford's "Waves" book from the Berkeley Physics Series, we stand outside about 40 meters from the wall of a three story building. One person claps and all listen for an echo. The rate of clapping is slowly increased, until a clap occurs at the same time as the echo from the previous clap, masking the echo.

The lab partner measures the time for 10 claps at this rate; 1/10 of that time is the round trip time for the sound pulse. We repeat this measurement, and use average and standard deviation of the results to estimate the best value and uncertainty in the round trip time. The distance to the wall is measured with 2 meter sticks, and its uncertainty is estimated also. From these results the best value for the sound velocity, and its uncertainty, are calculated.

The second measurement determines the phase velocity, using the usual resonance tube, whose air column length is adjusted by varying the level of water in the tube. We have tried small loudspeakers as the sound source, but a tuning fork, held so that the tines vibrate sideways, is still the most effective. We use rubber bands to mark the resonance position as the water level is slowly changed. From the separation between adjacent resonances we estimate the wavelength and its uncertainty, and accepting the tuning fork frequency as accurate, calculate the sound velocity and its uncertainty

Our confidence in the measurements is tested by noticing whether the two values for sound velocity agree within uncertainty limits.