Now This Is a Great Design

I usually begin our discussion of waves by tasking the students to design an experiment (as a class) to measure the speed of sound in air.  It's a backdoor way into experimental design, error analysis, and rate analysis, rather than really particularly wave-focused.  There are a variety of factors that make this difficult, not the least of which are the high speed of the wave (necessitating large distances) and the issue with measuring an event at a distance (made necessary by the large distance).

One of the slickest ways to get around this is by synchronizing watches, spreading out over a distance, and stopping the watches as each person hears a lour sound.  The differences between positions of the timers and the differences in times can be used to determine the speed - most easily by fitting a line to the position vs. time data, where the slope will give the speed, magically using all of the data in a single calculation!

A very creative design this year came from a couple of groups, actually:

• Stand some distance away from a wall
• Clap

... I've heard this one before, up to this point.  Generally, the problem comes when students try to measure the delay of that echo, which is really short.

• Clap again, when you hear the first echo
• Repeat, repeat, repeat...
• By counting claps and timing, say, 50 of them, determine the travel time for each echo.

That's a slick design, and applies some of the good measurement techniques that we've learned to apply to timing oscillations - nice work! It takes a few cycles to get your clapping tempo to match the travel period, but after you're synched up, you can take data on this pretty easily.

Our data:

• Average time of 13.43 seconds for 50 clap cycles (51 total claps!)
• Distance from the wall: 42.8 meters

There's an easy mistake to be made in the analysis, which a diagram will sort out:

The distance traveled during the time between claps is twice our measured distance; you have to make sure that the time and distance that you use to calculate the speed are for the same motion!

With an average travel time of .2686 seconds, and a distance traveled of 85.6 meters, our calculated speed of sound is... 319 meters per second!  That's pretty good for a really low-tech method, I'd say.