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Concepts Of Physics MCQ Edition [Volume 1]
Exam
Concepts Of Physics MCQ Edition [Volume 1]
Subject
Physics
Chapter
Sound Waves

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Sound Waves

A traffic policeman stationed on a road blows a whistle that emits...

A traffic policeman stationed on a road blows a whistle that emits a main frequency of 2.00 kHz2.00 \text{ kHz}. Determine the apparent frequency heard by a scooter-driver who is approaching the policeman at a speed of 36.0 km/h36.0 \text{ km/h}. The speed of sound in air is 340 m/s340 \text{ m/s}.

Options

  1. A2.06 kHz2.06 \text{ kHz}
  2. B1.94 kHz1.94 \text{ kHz}
  3. C2.21 kHz2.21 \text{ kHz}
  4. D1.79 kHz1.79 \text{ kHz}

Correct answer

A. 2.06 kHz2.06 \text{ kHz}

Step-by-step solution

The frequency of the source is f=2.00 kHzf = 2.00 \text{ kHz}.

The speed of the observer is vo=36.0 km/h=36.0×518 m/s=10.0 m/sv_o = 36.0 \text{ km/h} = 36.0 \times \dfrac{5}{18} \text{ m/s} = 10.0 \text{ m/s}.

The speed of sound is v=340 m/sv = 340 \text{ m/s} and the speed of the source is vs=0v_s = 0.

Using the Doppler effect formula for an observer approaching a stationary source:

f' = f \left(\dfrac{v + v_o}{v} \right)

Substituting the given values:

f′=2.00×(340+10340)f' = 2.00 \times \left( \dfrac{340 + 10}{340} \right)

f' = 2.00 \times \left(\dfrac{350}{340} \right)

f′=2.00×f' = 2.00 \times\dfrac{35}{34} \approx2.058 kHz2.058 \text{ kHz}

Rounding to two decimal places, f′≈2.06 kHz.f' \approx 2.06 \text{ kHz}.
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