A speaker fixed to a moving platform moves toward a wall, emitting a steady sound with a frequency of 245 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.

How fast should the platform move, vp, for the person to detect a beat frequency of 3.00 Hz?

by Doppler effect

F apparent = F real x (Vair + - Vobserver) / (Vair + - Vsource)

case1 : if observer is approaching a source then put a + in numerator and - in denominator

case 2 : if observer is going away from source then do opposite.

it is case1 cos observer is moving toward wall. actually wall is acting as a source for observer

so

F apparent = 240 x (344 + vp) / (344 - vp)

now F apparent - Freal = beat frequency of 6.00 Hz

so {240 x (344 + vp) / (344 - vp) } - 230 = 6

240 x (344 + vp - 344 + vp) / (344 - vp) = 6

240 x 2 x vp = 6 x (344 - vp)

480 vp = 2064 - 6 x vp

486 x vp = 2064

vp = 4.24 m/s