Question

As a racing car zooms by you, its pitch decreases by 20%. If the speed of sound is 345 m/s, how fast is the car travelling?

Answer 1

86m/s

Explanation

the frequency of a moving sound source appears to change according to a stationary observer, it is given by:

$\begin{gathered} f_{observer}=\frac{v_{sound}}{v\text{ sound }\pm v_{source}}\cdot f_{source} \\ \end{gathered}$

then

Step 1

Let

$\begin{gathered} v_{sound}=345\text{ m/s} \\ f_{source\text{ }}=0.8\text{Hz} \\ v_{source\text{ }}=v_s \\ f_{observer}=1.0\text{ Hz} \end{gathered}$

replace

$\begin{gathered} f_{observer}=\frac{v_{sound}}{v\text{ sound }\pm v_{source}}\cdot f_{source} \\ 0.8Hz=\frac{345\text{ }\frac{m}{s}}{345\text{ }\frac{m}{s}\text{ }\pm v_{source}}\cdot1.\text{z} \\ 0.8(345+v_s)=345\cdot1.0 \\ 276+0.8v_s=345 \\ \text{subtract 276in both sides} \\ 276+0.8v_s-276=345-276 \\ 0.8v_s=69 \\ v_s=\frac{69}{0.8}=86.25 \\ v_s=86\text{ }\frac{m}{s} \end{gathered}$

so, the answer is

86 m/s