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I am looking to experimentally measure the speed of sound using the Doppler Shift Equation with a stationary observer and moving source. The emitted frequency is constant, along with the speed of sound (unless there is a heat wave).

I am having trouble rearranging the formula in order to plot a straight line graph. Are there any particular arrangements which would give the wave speed (speed of sound) as the gradient on my straight line graph?

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  • $\begingroup$ Yes. What have you done so far? $\endgroup$
    – David White
    Apr 30, 2017 at 16:19

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Let's assume you know the speed $v$ of the source, and its frequency $f_0$. Then you will hear a sound with a frequency

$$ f = \frac{f_0}{1+\frac{v}{c}}$$

where $c$ is the speed of sound.

If $v \ll c$ then $f \approx f_0 (1 - \frac{v}{c})$ so the graph of $f(v)$ will be a line with a slope $-\frac{f_0}{c}$.

In the general case, you have $\frac{1}{f} = \frac{1}{f_0}(1 + \frac{v}{c})$, so $\frac{1}{f(v)}$ will be a straight line with a slope $\frac{1}{f_0 c}$.

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