Question

A submarine is fitted with a SONAR (Sound Navigation and Ranging) system which operates at an ultrasonic frequency of 42 kHz. An enemy submarine is moving towards the SONAR with a speed of 200 ms –1. If the speed of sound in seawater is 1400 ms–1, what is the frequency of sound received back at the SONAR fitted submarine after reflection from the enemy submarine?     

Solution

Correct option is

56 kHz

 

The frequency of ultrasonic (sound) waves sent out from the SONAR undergoes a change in two steps. (i) Before reflection, the frequency of sound received by the enemy submarine which is approaching the SONAR with a speed  is given by

                                              

(ii) The wave of frequency V’ is reflected from the enemy submarine, which acts as a virtual image source of frequency V’, approaching the SONAR with a speed . Hence the frequency of sound received back at the SONAR will be (observer stationary, source approaching)

                                           

SIMILAR QUESTIONS

Q1

A pipe of length 20 cm is open at both ends. Which harmonic mode of the pipe is resonantly excited by a 1700 Hz source? The speed of sound = 340 ms–1 

Q2

A wire has a mass 30 g and linear density 4 × 10 –2 kg m–1. It is stretched between two rigid supports and vibrates in its fundamental mode with a frequency of 50 Hz. What is the speed of transverse waves on the wire?

Q3

A steel rod of length 1.0 m is clamped rigidly at its middle. What is the frequency of the fundamental mode for the longitudinal vibrations of the rod? The speed of sound in steel = 5 × 103 ms –1 

Q4

Two tuning forks A and B produce 10 beats per second when sounded together. On slightly loading fork A with a little wax, it was observed that 15 beats are heard per second. If the frequency of fork B is 480 Hz, what is the frequency of fork A before it was loaded?

Q5

Two sitar strings A and B are slightly out of tune and produce beats of frequency 6 Hz. When the tension in string A is slightly decreased, the beat frequency is found to be reduced to 3 Hz. If the original frequency of A is 324 Hz, what is the frequency of B?

Q6

A metal wire of diameter 1 mm is held on two knife edges separated by a distance of 50 cm. The tension in the wire is 100 N. The wire vibrating with its fundamental frequency and a vibrating tuning fork together produce 5 beats per second. The tension in the wire is then reduced to 81 N. When the two are excited, beats are heard at the same rate. What is the frequency of the fork?

Q7

An ambulance blowing a siren of frequency 700 Hz is travelling slowly towards a vertical reflecting wall with a speed of 2 ms–1. The speed of sound is 350 ms–1. How many beats are heard per second?

Q8

Two persons A and B, each carrying a source of sound of frequency V, are standing a few metres apart in a quiet field. A starts moving towards Bwith a speed u. If v is the speed of sound, the number of beats heard per second by A will be

Q9

A train standing at a certain distance from a railway platform is blowing a whistle of frequency 500 Hz. If the speed of sound is 340 ms –1, the frequency and wavelength of the sound of the whistle heard by a man running towards the engine with a speed of 10 ms –1 respectively are      

Q10

A machine gun is mounted on a tank moving at a speed of 20 ms–1towards a target with the gun pointing in the direction of motion of the tank. The muzzle speed of the bullet equals the speed of sound = 340 ms–1. If, at the time of firing, the target is 500 m away from the tank, then