A speaker fixed to a moving platform moves toward a wall, emitting a steady sound with a frequency of 205 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 5.00 Hz?

Take the speed of sound to be 344 m/s.

The question relates to Doppler effect and beat.

The observer is moving towards the reflected sound so apparent frequency will be increased

f = f₀ x (V + v₁) / (V - v₂)

f is apparent frequency, f₀ is real frequency, V is velocity of sound, v₁ is velocity of observer and v₂ is velocity of source. Here

v₁ = v₂ = vp as both observer and source have same velocity

f = f₀ x (V + v₁) / (V - v₂)

205 + 5 = 205 x (344 + vp) / (344 - vp)

1.0234 = (344 + vp) / (344 - vp)

= 352 - 1.0234vp = 340+vp

12 / 2.0234vp

vp = 6 m / s approx.