# How do you use the Doppler Equation To Measure the Speed of Sound?

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?

• Yes. What have you done so far? – David White Apr 30 '17 at 16:19

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 $\frac{1}{f_0 c}$.