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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

In a calm sea, two submarines approach one another. Relative to the...

In a calm sea, two submarines approach one another. Relative to the water, the first submarine moves at 36 km h−136 \text{ km h}^{-1} while the second submarine moves at 54 km h−154 \text{ km h}^{-1}. The first submarine emits a sound signal (sonar) with a frequency of 2000 Hz2000 \text{ Hz}. Determine the frequency at which the second submarine receives this signal. Assume the speed of sound waves in water is 1500 m s−11500 \text{ m s}^{-1}.

Options

  1. A2020 Hz2020 \text{ Hz}
  2. B2034 Hz2034 \text{ Hz}
  3. C1967 Hz1967 \text{ Hz}
  4. D2013 Hz2013 \text{ Hz}

Correct answer

B. 2034 Hz2034 \text{ Hz}

Step-by-step solution

Speed of the first submarine (source), vs=36 km h−1=36×518 m s−1=10 m s−1v_s = 36 \text{ km h}^{-1} = 36 \times \dfrac{5}{18} \text{ m s}^{-1} = 10 \text{ m s}^{-1}

Speed of the second submarine (observer), vo=54 km h−1=54×518 m s−1=15 m s−1v_o = 54 \text{ km h}^{-1} = 54 \times \dfrac{5}{18} \text{ m s}^{-1} = 15 \text{ m s}^{-1}

Speed of sound in water, v=1500 m s−1v = 1500 \text{ m s}^{-1}

Actual frequency of the signal, f=2000 Hzf = 2000 \text{ Hz}

Using the Doppler effect formula for an approaching source and observer:

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

Substituting the given values:

f′=2000(1500+151500−10)f' = 2000 \left( \dfrac{1500 + 15}{1500 - 10} \right)

f' = 2000 \left(\dfrac{1515}{1490} \right)

f′=f' =\dfrac{303000}{149} \approx2033.56 Hz2033.56 \text{ Hz}

Rounding to the nearest integer gives 2034 Hz.2034 \text{ Hz}.
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