# Speed of sound: simple measurements

We made some simple measurements of the speed of sound in the multimedia chapter Sound. We also describe these in the lab section. These use time of flight. We'll see some more precise methods later on. This page gives background information and some details.

### A clap echo experiment

Here the camera and I were both 30 m from the wall of the building. My hands were 2 m from the camera and its microphone. So sound goes from my clapping hands via two different paths: by reflection from the wall, with a total distance of 60 m, or directly, 2 m. The difference in path is 58 m.

In this case, we can clearly see the clap and the echo in the sound track. However, I have amplified the echo in the sound track to make it more readily visible in this small screen sample Expanding the time scale, it's easy to measure to a precision of a couple of ms. The chief error is in deciding what features to recognise in the clap and echo. So sound has travelled the extra 58 m in 0.17 s, giving a speed of 340 m/s.

### Time of flight: light vs sound

Sound is much slower than light: 340 m/s vs 300,000,000 m/s. Nearly a million times slower. So the image arrives almost instantaneously. Here we compare the image and the sound of the collision of the wood blocks.

115 m takes me most of the way across a cricket field. But we still only have a few hundred ms. And the problem is that the camera only runs at 25 frames per second. Where on the soundtrack is the collision? To locate the collision on the soundtrack, I used the second and third images to estimate the speed of the blocks and used that to position the collision between the second and third frame. This gives a time delay of 0.34 s, and so again a speed of 340 m/s. The interpolation is only one concern in this experiment: we also didn't know how the camera labelled images with times. So the echo experiment above is, we think, more reliable.

### Two microphones and a long cable

The next experiment will use a long cable. Actually we used all the long cables from our lab and from a nearby lab and connected them together to give us a total length of 34 m. We know that coaxial cables both slow the electric signal and attenuate the high frequencies - though of course high frequency here means high radio frequencies. Can this be detected in the sound? Probably not, but worth demonstrating. So we conneceted one microphone to one channel, and the other microphone via the 34 m cable to the other channel.

Not much difference. No surprise. For the original cable under the Atlantic Ocean, however, attenuation and delays were very significant and limited telegraph speeds to less than a word per minute.

### Time of flight with a cable

Here we used two microphones, 33.03 m apart. Again, the weaker signal has been amplified to make it easier to see on the soundtrack. The delay is 96 ms, which gives a speed of 340 m/s.

### Effect of transmission through air?

This experiment was not a convincing one. What we wanted to do was to compare the timbre of sound that had travelled 30 m through air with one that had travelled less that one metre. The left channel travels one metre through air then 30 m through the cable. The right channel signal travels 30 m through the air and 2 m through cables. Again, similar microphones.

Because of nonadiabatic losses in transmission, high frequencies are attenuated more than low and, at 30 m, we calculated that one might expect to hear a difference. Provided, of course that the background noise doesn't mask the differences. Briefly, the campus is near the city, has abundant bird-life and is near to the coast so that wind is rarely less than a few knots. By the time that we'd lay out a cable, students or gardeners would appear.... Okay, if you know a really quiet, open location and can lay your hands on several tens of metres of coaxial cable and two microphones, we'd like to hear from you!