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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