JEE Advanced 2024 Paper 1 · Q11 · Sound Waves
A source (S) of sound has frequency 240 Hz. When the observer (O) and the source move towards each other at a speed $v$ with respect to the ground (as shown in Case 1 in the figure), the observer measures the frequency of the sound to be 288 Hz. However, when the observer and the source move away from each other at the same speed $v$ with respect to the ground (as shown in Case 2 in the figure), the observer measures the frequency of sound to be $n$ Hz. The value of $n$ is _____.
Reveal answer + step-by-step solution
Correct answer:200
Solution
Doppler effect: speed of sound $v_s$, source and observer each move at speed $v$. Case 1 (approaching): $f_1 = f_0\,\dfrac{v_s + v}{v_s - v}$ ⇒ $288 = 240\cdot\dfrac{v_s + v}{v_s - v}$, so $\dfrac{v_s + v}{v_s - v} = \dfrac{288}{240} = \dfrac{6}{5}$, giving $5(v_s + v) = 6(v_s - v)$ ⇒ $v_s = 11v$. Case 2 (receding): $f_2 = f_0\,\dfrac{v_s - v}{v_s + v} = 240\cdot\dfrac{11v - v}{11v + v} = 240\cdot\dfrac{10}{12} = 240\cdot\dfrac{5}{6} = 200$ Hz. Therefore $n = 200$.
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