Speed-of-sound measurements
done by Ms. Irving's 6th-grade class
First we did the time measurements. Among the children, there were 4 watches, Ms. Irving had one, and I had brought one, plus an alarm clock with a second hand. Some watches had old-fashioned faces that could be observed by more than one person. I did the tapping, and the kids counted taps in a convenient 15-second interval. We got the following counts: 16, 16, 15, 16, 15, 16, 17, 17. The average is 16.0 counts in 15 seconds, or 0.94 second between beats.
Next we measured the distance to the wall.I had brought one 12-foot tape measure, and there were a number of them from the classroom. I explained how they could measure a few steps, and then count steps to the wall. The class spontaneously broke up into teams of 2 and 3, and went to work. These are the measurements we recorded:
Steps to the wall | How big is a step? | Feet to the wall | Sound speed | ||
---|---|---|---|---|---|
feet/sec | mph | ||||
Aisha | 108 | 3 steps = 84" | 252' | 1075 | 733 |
Kim | 117 | 5 steps = 12' | 281' | 1199 | 817 |
Dennis | 217 (roundtrip) | 1 step = 2'3" | 244' | 1041 | 710 |
Sam | 123 | 4 steps = 85" | 218' | 930 | 634 |
Kelly | 102 | 1 step=1'8" | 170' | 725 | 494 |
Trey | 114 | 1 step = 2' | 228' | 972 | 663 |
Celeste | 104 | 1 step = 20" | 173' | 738 | 502 |
Ms. Irving | 218 (roundtrip) | 10 steps = 19'2" | 209' | 892 | 608 |
Pearl & Kathryn | 116 | 3 steps = 5' | 193' | 823 | 561 |
[There were actually more counts, but not all got calibrated, and not
all got written down - apologies to the kids that I missed]
Columns 2 and 3 are what was measured. From that, the distance to the wall
was calculated (column 4).
In the time between the BANG and the returning echo, the sound has traveled
to the wall and back. Since the echo is halfway between BANGS, the sound
travels 4 times the distance to the wall in the time between BANGS on the
can. Therefore the speed of sound is 4x what is in column 4, divided by
the time we measured, 0.94 seconds. The result is written in column 5,
which is the speed of sound in feet/second. The last column is this speed
converted to miles per hour.
You can see from the table that there is a great spread in the estimates
of the distance, which translates into a proportional spread in the final
results.
Nevertheless, all results are in the right ballpark (about 1115 ft/s
or 760 mph), and I think they all got the hang of how to do rough
measurements quickly. Recall that we did the whole thing in a 1-hour time
slot.