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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 behind the car. The speed of sound in air is 340 m/s340 \text{ m/s}.

Options

  1. A1181 Hz1181 \text{ Hz}
  2. B1324 Hz1324 \text{ Hz}
  3. C1250 Hz1250 \text{ Hz}
  4. D1328 Hz1328 \text{ Hz}

Correct answer

A. 1181 Hz1181 \text{ Hz}

Step-by-step solution

Speed of the car, 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, f=1250 Hzf = 1250 \text{ Hz}

Since the car is moving away from the stationary observer, the apparent frequency f′f' is given by the Doppler effect formula:

f′=f(vv+vs)<br><br>f' = f \left( \dfrac{v}{v + v_s} \right)<br><br>f' = 1250 \left( \dfrac{340}{340 + 20} \right)

f′=1250(340360)f' = 1250 \left( \dfrac{340}{360} \right)

f′=1250×1718f' = 1250 \times \dfrac{17}{18}

f′≈1180.55 Hz≈1181 Hzf' \approx1180.55 \text{ Hz} \approx1181 \text{ Hz}
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