Question

A speaker fixed to a moving platform moves toward a wall, emitting a steady sound with a frequency of 225 Hz . A person on the platform right next to the speaker detects the sound waves reflected off the wall and those emitted by the speaker. Part A How fast should the platform move, vp, for the person to detect a beat frequency of 7.00 Hz ? Take the speed of sound to be 344 m/s. Express your answer

Answer 1

To solve this problem it is necessary to apply the concepts related to the Doppler effect. The frequency would be defined as

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

Where,

c = 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

$f_0$= emitted frequency

Our values are given as,

Beat frequency = 7Hz

Reflective Doppler frequency = 225+7=232Hz

Speed of sound (c) = 344m/s

$f = 232Hz\\f_0 = 225Hz\\V_r = V_s$

Replacing,

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

$232 = \frac{c+v_r}{c-v_r}(225)$

$232(c-v_r)= 225(c+v_r)$

$232c-232v_r = 225c+225v_r$

$232c-225c = 232v_r+225v_r$

$7c = 457v_r$

$v_r = \frac{7*344}{457}$

$v_r = 5.268m/s$

Therefore the platform move around 5.268m/s