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.

Explanation:

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.

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