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 = (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 = (c + v_r)/(c - v_s)f_0`

`f = (343 + 14.8)/(343 - 32)(523)`

`f = 601.7Hz`

Therefore the frequency that hear the motorcyclist is 601.7Hz