# Speed of Sound

I just completed a lab in which we created standing waves in a fixed length of pipe using a function generator. An oscilloscope was used to measure the amplitude of the waves. The frequency was changed until a resonant condition was met, and then the location of all the nodes/antinodes was measured. We used the distance from antinode to antinode to measure the wavelength of the wave. (One wavelength = 2X the distance measured). This was repeated for two additional frequencies.

Once we had this information, we calculated the velocity of the waves using the equation:
v = frequency * wavelength.

These values were then compared to the "actual" speed of sound, as calculated from the equation v = 331.5 +.607(T), where T was 24 Celsius.

So here's my question: The calculated velocity of the first standing wave was smaller than the "actual" velocity. The calculated velocity of the second and third standing waves was BIGGER than the "actual" velocity. What explains this? Can the difference be attributed to human error in measuring the distance between antinodes or is there some physical phenomenon going on?

## Answers and Replies

Doug Huffman
Gold Member
The first error source I would suspect is your "equation" model. I see, for instance, no consideration of the stiffness of the pipe. I see no mention of the size of the error or the measuring protocol. Was the error consistent across the many students' project?

As I recall my freshman physics class, the bulk of the lab lecture was on evaluating the errors.

All experiments are subject to systematic and random errors.When using your results to calculate the speed you should,ideally,have estimated the percentage error and expressed the results accordingly eg speed of sound=330m/s+or-5%.Even what you called the "actual velocity" cannot be measured to absolute accuracy and precision.Taking errors into account there should be overlap between the "actual velocity" and the calculated velocity.

The first error source I would suspect is your "equation" model. I see, for instance, no consideration of the stiffness of the pipe. I see no mention of the size of the error or the measuring protocol. Was the error consistent across the many students' project?

As I recall my freshman physics class, the bulk of the lab lecture was on evaluating the errors.

I suspect also that something like lycopodium powder was used and if so the would be large errors in measuring the internodal distances.