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BITSAT 2022 Paper

Section: Physics

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Question : 3 of 130

Marks: +1, -0

A submarine

A

17\,\mathrm{m/s}

is being chased along the line of its velocity by another submarine

B

34\,\mathrm{m/s}

. B sends a sonar signal of

600\,\mathrm{Hz}

A

and receives a reflected sound of frequency

v

v

[Speed of sound in water

=1500\,\mathrm{ms}^{-1}

$613.7\,\mathrm{Hz}$
$6137\,\mathrm{Hz}$
$62\,\mathrm{Hz}$
$539\,\mathrm{Hz}$

Solution: 👈: Video Solution

Given, velocity of submarine

A,\; v_A17\,\mathrm{m/s}

Velocity of Submarine

B,\; v_B = 34\,\mathrm{m/s}

Signal sent by submarine B is detected by submarine

A

can be shown as

Frequency of the signal,

f_0=600\,\mathrm{Hz}

speed of sound in water

v_s=1500\,\mathrm{ms}^{-1}

Frequency received by submarine

A

is

f_1 = \frac{v_S-v_A}{v_S-v_B} f_0 = \left[\frac{1500-17}{1500-34}\right] \times 600\,\mathrm{Hz}

f_1 = \frac{1483}{1466} \times 600 \ \dots\ (i)

Frequency received by submarine is

f_2 = \frac{v_S+v_B}{v_s - v_A} f_1

Substituting given values and

f_1

value from Eq. (i), we get

f_2 = \frac{1500+34}{1500+17} \times \left[\frac{1483}{1466} \times 600\right]

f_2 = 1.0112 \times 1.0115 \times 600

f_2 = 613.7\,\mathrm{Hz}

.

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