1. Estimate the speed of sound

Introduction

The first project in this series uses the recording and waveform display capabilities of Raven Lite to estimate the speed of sound. 

Discussion of the theoretical model

We can estimate the speed of sound in air by measuring the time it takes for a sound impulse to travel a known distance.  Then

c=\frac{known distance}{time to travel the distance}

This could be done using two microphones spaced the known distance apart but we will use a single microphone to capture the initial impulse of a breaking balloon and then will capture the return impulse after it reflects off of a large wall.

The experiment

This measurement is made outdoors in a yard or parking lot next to a single large building.  The idea is to find a space that has one large vertical reflecting surface and no others.  Measure off a distance perpendicular to the wall of exactly 100 feet and place the microphone at that point.

Inflate a rubber balloon and start Raven Lite recording to memory.   Quickly prick the balloon with a needle to pop it.  Stop the recording and save it to disk.  Make a couple of repeat recordings.

Interpreting the results

You should see something that looks like this:

 speedimg

Use the mouse to position the pointer over each impulse to read the time at the lower left corner of the screen.

I got 10.431 seconds on the direct impulse and 10.612 seconds on the tiny reflected impulse for a difference of 0.181 seconds.  This is the time required to go 200 feet.  Calculating the speed from those values gives an estimate of 1104.97 ft/second.

The temperature this morning was 40 ° F = 4.44 ° C = 277.4 ° K.  At that temperature the speed of sound should be

c=331 \sqrt {\frac {T}{273}}=333.66 \frac{meters}{sec}=1094.7 \frac{ft}{sec}

Our estimate is a little bit off, but being within 1% is not bad.  Two obvious things contribute.  First, a thousandth of a second makes a significant difference in the speed estimate and it is difficult to measure the two times precisely due to the resolution of Raven Lite and the breadth of the signal on the display.  Repeated measurements could be done to average out this error.  Second, my microphone was at ground level since I just have a little desktop stand for it but I was standing when I broke the balloon.  The time it took for the direct sound to reach the microphone is not insignificant and should be accounted for.

4 thoughts on “1. Estimate the speed of sound

  1. Mic

    Humidity and barometeric pressure should have some effect on the speed but I don’t know how much. Speed of the A to D may need to be considered if you are going to start splitting hairs.

    You have all the fun!

  2. Ron,
    My old acoustics book, Kinsler and Frey, 2nd edition, develops the equations of motion for sound in fluids in Chapter 5. They state pretty categorically in section 5.5 that the velocity of sound doesn’t change with barometric pressure. They go on to say that “…the changes in velocity that result from the changes in temperature are of much greater significance than those resulting from the inhomogeneity in composition.” I take that to include the humidity.

    I need to do this experiment again. I have considered some of the sources of error and ways to deal with them. I made the measurement in a church parking lot one Saturday morning about 8:45. It was great. I got all set up and made one measurement when the pastor and another guy came out to find out what I was doing with a computer and a bunch of balloons in their parking lot. The pastor was interested but the other guy kinda moved away from me. It turned out that they were have some kind of big youth gathering at 9:00. I packed up and left as the parking lot began to fill with speeding teenage drivers…I only got one test done.

    Thanks for taking time to look at the recent additons to the site…

  3. Nice application of Raven Lite. Thanks for sharing this. In Raven Lite, the mouse cursor will always report 3 digits of precision, but you can get 6 digits past the decimal point on the time axis if you’re zoomed in far enough in time. This should help reduce the time error by increasing your resolution. I have a screen capture that I can post, but I don’t see an interface for attaching images here. Raven Lite records at 44100 Hz, which means that there is one sample taken every 1/44100 = 22.676 microseconds, so that would be your limit on precision with the current configuration. In Raven Pro, you can alter the sample rate and also get measurements in the selection table, which allows you to choose the number of digits of precision on a per column basis.

    Tim (Raven software developer)

  4. Thanks for your comments Tim. I keep thinking I will repeat this exercise with multiple runs and more careful execution to see how close to the accepted value I can get…knowing that I can get a few more digits of precision might help get me moving on it.

    Raven Lite is a wonderful piece of software…easy to use, runs on all the popular computing platforms, is capable of demonstrating all kinds of interesting acoustical phenomena and information, and it’s free of charge. It’s my “go to” software for exploring sounds I record and I have gotten a lot of enjoyment out of it over the past few years. I remember how excited I got when I first “discovered” the Doppler shift signature and more recently the multi-path interference signature in the spectrogram. Thanks for making it available.

    Mic

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