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 :

Question

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) 753 Hz (B) 500 Hz (C) 333 Hz (D) 666 Hz

Tardigrade Admin · Accepted Answer

Frequency of the sound produced by flute,

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

Velocity of observer,

v_{0} = 10 \times \frac{5}{18} = \frac{25}{9} m / s

∴

frequency detected by observer, f' =

[\frac{v + v _{0}}{v}] f

∴ f^{'} = [\frac{\frac{25}{9} + 330}{330}] 660

=

335.56 \times 2 = 671.12

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

753 Hz

500 Hz

333 Hz

666 Hz

Frequency of the sound produced by flute, f=2(2ℓv​)=2×0.52×330​=660Hz Velocity of observer, v0​=10×185​=925​m/s ∴ frequency detected by observer, f' = [vv+v0​​]f ∴f′=[330925​+330​]660 = 335.56×2=671.12

Q. A musician using an open flute of length $50 c m$ 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 :