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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 person travelling in a car moving at 72 km/h blows a whistle that...

A person travelling in a car moving at 72 km/h72 \text{ km/h} blows a whistle that emits a wave of frequency 1250 Hz1250 \text{ Hz}. Determine the frequency heard by another person standing on the road in front of the car. The speed of sound in air is 340 m/s340 \text{ m/s}.

Options

  1. A1328 Hz1328 \text{ Hz}
  2. B1176 Hz1176 \text{ Hz}
  3. C1250 Hz1250 \text{ Hz}
  4. D1181 Hz1181 \text{ Hz}

Correct answer

A. 1328 Hz1328 \text{ Hz}

Step-by-step solution

Speed of the car (source), vs=72 km/h=72×518 m/s=20 m/sv_s = 72 \text{ km/h} = 72 \times \dfrac{5}{18} \text{ m/s} = 20 \text{ m/s}

Speed of sound, v=340 m/sv = 340 \text{ m/s}

Actual frequency of the whistle, f0=1250 Hzf_0 = 1250 \text{ Hz}

Since the car is moving towards the stationary observer, the apparent frequency ff is given by the Doppler effect formula:

f = f_0 \left(\dfrac{v}{v - v_s} \right)

Substituting the given values:

f=1250(340340−20)f = 1250 \left( \dfrac{340}{340 - 20} \right)

f = 1250 \left(\dfrac{340}{320} \right)

f=1250×f = 1250 \times\dfrac{17}{16}

f=1328.125 Hzf = 1328.125 \text{ Hz}

The frequency heard by the person is approximately 1328 Hz1328 \text{ Hz}.
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