Question

An airplane traveling at half the speed of sound emits a sound of frequency 4.68 kHz. (a) At what frequency does a stationary listener hear the sound as the plane approaches? kHz (b) At what frequency does a stationary listener hear the sound after the plane passes? kHz

Answer 1

Answer:

(a) 9.36 kHz

(b) 3.12 kHz

Explanation:

(a)

V = speed of sound

$v$ = speed of airplane = (0.5) V

f = actual frequency of sound emitted by airplane = 4.68 kHz = 4680 Hz

f' = Frequency heard by the stationary listener

Using Doppler's effect

$f' = \frac{Vf}{V-v}$

$f' = \frac{V(4680)}{V-(0.5)V)}$

f' = 9360 Hz

f' = 9.36 kHz

(b)

V = speed of sound

$v$ = speed of airplane = (0.5) V

f = actual frequency of sound emitted by airplane = 4.68 kHz = 4680 Hz

f' = Frequency heard by the stationary listener

Using Doppler's effect

$f' = \frac{Vf}{V+v}$

$f' = \frac{V(4680)}{V+(0.5)V)}$

f' = 3120 Hz

f' = 3.12 kHz