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

yes..........................................

Step-by-step explanation:

yes...........................................

Answer 2

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{ }(m)/(s)}{345\text{ }(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=(69)/(0.8)=86.25 \\ v_s=86\text{ }(m)/(s) \end{gathered}`

so, the answer is

86 m/s