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AP EAMCET201923 Apr 2019Morning ShiftPhysicsWaves and SoundActual

A police car moving at (22 ~ms ⁻¹ ) chases a motor cyclist. The police man sounds horn at (176 ~Hz ), while both of them move towards a stationary siren of frequency (165 ~Hz ). If the number of beats heard by the motor cyclist per second is zero, then the speed of motorcycle is ( Speed of sound in air (=330 ~ms ⁻¹ ))

Options

  1. A(33 ~ms ⁻¹ )
  2. B(22 ~ms ⁻¹ )
  3. C(44 ~ms ⁻¹ )
  4. D(11 ~ms ⁻¹ )

Correct answer

B. (22 ~ms ⁻¹ )

Step-by-step solution

According to the question, we draw the following situation, Given, velocity of car, (v_ s₁ =22 ~ms ⁻¹ ) speed of the sound in air, (v=330 ~ms ⁻¹ ) apparent frequency by cyclist from the police car, ( aligned f₁^ & = v-v₀ v-v_s f₁ f₁^ = 330-v₀ 330-22 176 & = 330-v₀ 308 176 aligned ) apparent frequency by cyclist from the stationary siren, (f₂^ = v+v₀ v f₂= 330+v₀ 330 165 ) Number of beats heard by the cyclist, ( aligned & n=f₁^ -f₂^ =0 (Given, n=0 ) & f₁^ =f₂^ & (330-v₀ ) 176 308 = (330+v₀ ) 165 330 & v₀=22 ~ms ⁻¹ a

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