How to measure sound frequency

How to measure sound frequency

Shake one end of a rope to create a wave. You can tell the wavelength of this wave easily. It is the distance between adjacent crests. So just measure it with a ruler.

Sound is a wave travelling through air. We cannot see the oscillations of the pressure or the air molecules. How can we measure the wavelength of sound?

The answer is: we make use of the different phases of the oscillations at different points along the wave, and display the two oscillations on an oscilloscope.

To explain what this means, I shall first illustrate the idea using the rope wave.

The solid curve above is a snapshot of the rope wave at a certain time. After a short time, the wave travels to the position of the dashed curve. Look at the point at 0. It moves up and down with time. A graph of the displacement of this point against time is shown as the solid curve below. Then look at the point A just next to 0 above. A graph for A against time is shown in the dotted curve below. Thus we see that the displacement-time graphs for two points at different positions along the rope are out of phase.

As point A in the first graph moves further from 0, so the dotted curve in the second graph moves further from the solid curve. However, when point A in the first graph reaches a distance of one wavelength from 0, the dotted curve in the second graph coincides with the solid curve.

Conversely, if the dotted curve in the second graph coincides with the solid curve, then we know that the two points 0 and A in the first graph are separated by one wavelength. This is tells us how to use the oscilloscope to find the wavelength.

We also need two microphones. I have explained how a microphone and an oscilloscope work in the page on measuring sound frequency. Here, I shall just assume that a microphone can detect the sound at a certain point in the air, and the oscilloscope can plot a graph of the pressure against time at that point. If I have two microphones separated by a small distance, and both connected to the oscilloscope, the we would see two graphs that look quite similar to the second graph above.

Now, move one microphone slowly away from the other microphone, and in the direction of the sound. Look the two curves in the second figure above. Focus on one of the crests on the dotted curve. The two traces (curves) on the oscilloscope would initially move a part, as in the second graph above. After some time, a crest on the dotted curve would arrive at the next crest on the solid curve. This oscillations at the microphones are now in phase. This would only happen if the distance between the microphones is equal to the wavelength of the sound.

Stop moving the microphone and measure the distance between the two microphones. This is the wavelength.

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