Two submarines are approaching each other in a calm sea. The first submarine travels at a speed of 36 km $h^{- 1}$ and the other at 54 km $h^{- 1}$ ' relative to the water. The first submarine sends a sound signal (sound waves in water are also called sonar) at a frequency of 2000 Hz. (a) At what frequency is this signal received by the second submarine ? (b) The signal is reflected from the second submarine. At what frequency is this signal received by the first submarine. Take the speed of the sound wave in water to be $1500 m s^{- 1}$

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Solution

According to the question,

v=1500 m/s f=2000 Hertz $v_{s} = 10$ m/s, $v_{0} = 15$ m/s

So, the apparent frequency heard by the submarine B

$= (\frac{1500 + 15}{1500 - 10}) \times (2000)$

=2034 Hz

(b)Apparent frequency received by submarine A

$= (\frac{1500 + 10}{1500 - 15}) \times (2034)$

=2068 Hz

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Q. Two submarines are approaching each other in a calm sea. The first submarine travels at a speed of 36 km h⁻¹ and the other at 54 km h⁻¹ relative to the water. The first submarine sends a sound signal (sound waves in water are also called sonar) at a frequency of 2000 Hz. (a) At what frequency is this signal received from the second submarine. At what frequency is this signal received by the first submarine. Take the speed of of the sound wave in water to be 1500 m s⁻¹.

A SONAR system fixed in a submarine operates at a frequency 40.0 kHz. An enemy submarine moves towards the SONAR with a speed of 360 km h^–1. What is the frequency of sound reflected by the submarine? Take the speed of sound in water to be 1450 m s^–1.

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(B)

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and receives a reflected sound of frequency

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A sonar device on a submarine sends out a signal and receives an echo 5 s later. Calculate the speed of sound in water if the distance of the object from the submarine is 3625 m.

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According to the question, v=1500 m/s f=2000 Hertz vs=10 m/s, v0=15 m/s So, the apparent frequency heard by the submarine B =(1500+151500−10)×(2000) =2034 Hz (b)Apparent frequency received by submarine A =(1500+101500−15)×(2034) =2068 Hz