Question

A motorcycle and a police car are moving toward one another. The police car emits sound with a frequency of 523 Hz and has a speed of 32.2 m > s. The motorcycle has a speed of 14.8 m > s. What frequency does the motorcyclist hear?

Answer 1

To solve this problem it is necessary to apply the concepts related to Dopler's Law. Dopler describes the change in frequency of a wave in relation to that of an observer who is in motion relative to the Source of the Wave.

It can be described as

$f = \frac{c\pm v_r}{c\pm v_s}f_0$

c = Propagation speed of waves in the medium

$v_r$= Speed of the receiver relative to the medium

$v_s$= Speed of the source relative to the medium

$f_0 =$Frequency emited by the source

The sign depends on whether the receiver or the source approach or move away from each other.

Our values are given by,

$v_s = 32.2m/s \rightarrow$ Velocity of car

$v_r = 14.8 m/s \rightarrow$ velocity of motor

$c = 343m/s \rightarrow$ Velocity of sound

$f_0 = 523Hz \rightarrow$Frequency emited by the source

Replacing we have that

$f = \frac{c + v_r}{c - v_s}f_0$

$f = \frac{343 + 14.8}{343 - 32}(523)$

$f = 601.7Hz$

Therefore the frequency that hear the motorcyclist is 601.7Hz