Question

A speaker fixed to a moving platform moves toward a wall, emitting a steady sound with a frequency of 230Hz. A person on the platform right next to the speaker detects the sound waves reflected off the wall and those emitted by the speaker.
How fast should the platform move (in m/s) ,v_p, for the person to detect a beat frequency of 1.00Hz? Take the speed of sound to be 344m/s.

Answer 1

Answer:

$v_s = 0.746\ m/s$

Explanation:

given,

frequency emitted by the speaker(f) = 230 Hz

beat frequency = 1 Hz

speed of the sound (v)= 344 m/s

velocity of the platform = ?

frequency heard by the observer

 f_d = 230 Hz + 1 Hz

 f_d = 231 Hz

using ,

$f_d = \dfrac{f(v + v_s)}{v-v_s}$

$231 = \dfrac{230(344 + v_s)}{344-v_s}$

$231 (344- v_s) = 230(344 + v_s)$

$(231 -230)344= 230 v_s + 231 v_s$

$344= 461 v_s$

$v_s = 0.746\ m/s$