A locomotive travels along a straight path at a constant speed of 20text ms ^ -1 while sounding its whistle at 1000text Hz . Calculate the approximate percentage change in frequency perceived by a stationary observer as the locomotive passes them. (Speed of sound = 320text ms ^ -1 ).

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EEJ MAIN Physics QUESTION #7030

Question 1

A locomotive travels along a straight path at a constant speed of $20\text{ ms}^{-1}$ while sounding its whistle at $1000\text{ Hz}$. Calculate the approximate percentage change in frequency perceived by a stationary observer as the locomotive passes them. (Speed of sound $= 320\text{ ms}^{-1}$).

$6\%$
$12\%$✔️
$18\%$
$24\%$

Correct Answer Explanation

Using the Doppler effect: Frequency approaching $f_{app} = f(\frac{v}{v - v_s}) = 1000(\frac{320}{300}) \approx 1066.6\text{ Hz}$. Frequency receding $f_{rec} = f(\frac{v}{v + v_s}) = 1000(\frac{320}{340}) \approx 941.1\text{ Hz}$. The change is $\approx 125.5\text{ Hz}$. Percentage change relative to the source is $(\frac{125.5}{1000}) \times 100 \approx 12.5\%$.

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