Question 344: Waves

Question

The pitch of a whistle of an engine appears to drop by $30 \%$ of original value when it passes a stationary observer. If the speed of sound in air is $350 \mathrm{~ms}^{-1}$, then the speed of engine in $\mathrm{ms}^{-1}$ is

Accepted Answer

To solve this problem, we use the Doppler effect formula for sound when the source is moving and the observer is stationary:
$$ f' = f \frac{v}{v + v_s} $$
where:
$ f' $ is the observed frequency,
$ f $ is the original frequency,
$ v $ is the speed of sound in air,
$ v_s $ is the speed of the source (engine).
Given that the pitch drops by 30%, the new frequency is:
$$ f' = 0.7f $$
Substitute this into the Doppler equation:
$$ 0.7f = f \frac{350}{350 + v_s} $$
Cancel $ f $ from both sides:
$$ 0.7 = \frac{350}{350 + v_s} $$
Rearrange to solve for $ v_s $:
$$ 0.7(350 + v_s) = 350 $$
Expand:
$$ 245 + 0.7v_s = 350 $$
Subtract 245 from both sides:
$$ 0.7v_s = 105 $$
Divide by 0.7:
$$ v_s = \frac{105}{0.7} = 150 	ext{ m/s} $$
Thus, the speed of the engine is $ \boxed{150} 	ext{ m/s} $.

Answer

840

Answer

700

Answer

175

Answer

150

Waves

The pitch of a whistle of an engine appears to drop by 30 \% of original value when it passes a stationary observer. If the speed of sound in air is 350 \mathrm{~ms}^{-1}, then the speed of engine in \mathrm{ms}^{-1} is

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