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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 car's horn emits sound having a dominant frequency of 2400 Hz ....

A car's horn emits sound having a dominant frequency of 2400 Hz2400 \text{ Hz}. Determine the apparent dominant frequency heard by a person standing on the road ahead of the car, given that the car approaches at 18.0 km/h18.0 \text{ km/h}. The speed of sound in air is 340 m/s340 \text{ m/s}.

Options

  1. A2436 Hz2436 \text{ Hz}
  2. B2534 Hz2534 \text{ Hz}
  3. C2365 Hz2365 \text{ Hz}
  4. D2273 Hz2273 \text{ Hz}

Correct answer

A. 2436 Hz2436 \text{ Hz}

Step-by-step solution

The speed of the car (source) is vs=18.0 km/h=18.0×518 m/s=5 m/sv_s = 18.0 \text{ km/h} = 18.0 \times \dfrac{5}{18} \text{ m/s} = 5 \text{ m/s}.

The observer is stationary, so vo=0v_o = 0.

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

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

Substituting the given values:

f′=2400(340340−5)f' = 2400 \left( \dfrac{340}{340 - 5} \right)

f' = 2400 \left(\dfrac{340}{335} \right)

f′≈2435.8 Hzf' \approx 2435.8 \text{ Hz}

Rounding to the nearest integer, the apparent frequency is 2436 Hz.2436 \text{ Hz}.
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