A musician using an open flute of length 50 cm produces second harmonic sound waves. A person runs towards the musician from another end of a hall at a speed of $10 \mathrm{~km} / \mathrm{h}$. If the wave speed is $330 \mathrm{~m} / \mathrm{s}$, the frequency heard by the running person shall be close to:

JEE Main · 2019 · 09 Jan 2019 · Shift 2 · Waves & Sound

A musician using an open flute of length 50 cm produces second harmonic sound waves.
A person runs towards the musician from another end of a hall at a speed of

10 km / h

. If the wave speed is

330 m / s

, the frequency heard by the running person shall be close to:

(A)666 Hz✓ Correct
(B)753 Hz
(C)500 Hz
(D)333 Hz

Answer: (A)

Solution

The open flute of length

ℓ = 0.5 m

in its second harmonic emits

f = \frac{2 v}{2 ℓ} = \frac{v}{ℓ} = \frac{330}{0.5} = 660 Hz

. The listener runs toward the stationary source at

v_{o} = 10 km/h = \frac{50}{18} \approx 2.78 m/s

, so by the Doppler formula for a moving observer

f^{'} = f \frac{v + v _{o}}{v} = 660 (\frac{330 + 2.78}{330}) \approx 666 Hz

JEE Main · 2019 · 09 Jan 2019 · Shift 2 · Single correct option

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