Question

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 ms^-1.

Answer 1

Here, frequency of SONAR (Source) = 40 kHz = 40 x 10³ Hz

Speed of sound waves (v) = 1450 ms^-1

Speed of the observer, (v₀) = 360 km h^-1

= 360 x 5/18 ms^-1 = 1000 ms^-1

Since the source is at rest and the observer moves towards the source (SONAR)

We have,

This frequency (v') is reflected by the enemy ship and is observed by the SONAR (which now acts as observer). Therefore, in the case, v_s = 360 km h^-1 = 100 ms^-1

Apparent frequency,