Question

A factory siren indicating the end of a shift has a frequency of 80 Hz where the speed of sound in air is 343 m/s. What frequency is perceived by the occupant of a car that is traveling at 30 m/s (a) towards the factory and (b) away from the factory

Answer 1

To develop this problem it is necessary to apply the concepts related to the Dopler Effect.

The apparent frequency can be calculated through the expression

$f' = \frac{v\pm v_0}{v}*f$

Where,

v = Velocity of the sound or light

$v_0 =$Velocity of the observer

f=Real frequency

Our values are given as,

$v = 343m/s$

$v_0 = 30m/s$

$f = 80Hz$

PART A ) Towards the factory we need to apply the plus sign

$f' = \frac{v+v_0}{v}*f$

$f' = \frac{343+30}{343}*80$

$f' = 86.99Hz$

PART B ) Away from the factory we need to apply the minus sign

$f' = \frac{v-v_0}{v}*f$

$f' = \frac{343-30}{343}*80$

$f' = 73 Hz$