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' = (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' = (v+v_0)/(v)*f`

`f' = (343+30)/(343)*80`

`f' = 86.99Hz`

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

`f' = (v-v_0)/(v)*f`

`f' = (343-30)/(343)*80`

`f' = 73 Hz`