Question

The pitch of the whistle of an engine appears to drop by 20% of its original value when it passes a stationary observer. If the speed of sound in the air is 350 m/s, then the speed of the engine (in m/s) is ______.

Options

• 1050

• 175

• 520.5

• 87.5

Answer 1

The pitch of the whistle of an engine appears to drop by 20% of its original value when it passes a stationary observer. If the speed of sound in the air is 350 m/s, then the speed of the engine (in m/s) is 87.5.

Explanation:

Given, the speed of sound, v_s = 350 m/s

Since the pitch of the sound produced by the whistle depends on frequency (f).

Hence, f' = f - 20% of f' = `4/5`f

⇒ `f^'/f = 4/5`

Also, `f^'/f = "v"_s/("v"_s + "v"_e)`

where, v_e = speed of engine

⇒ `4/5 = 350/(350 + "v"_e) ⇒ 350 + "v"_e = 5/4 xx 350`

⇒ `"v"_e = 350(5/4 - 1) = 350/4 = 87.5` m/s