Question

. Active sonar is used to determine the speed of an oncoming submarine. You send out a signal with a frequency of 500.0Hz. Your submarine is traveling at 13.0 m/s and the enemy is coming towards you at 9.00 m/s. Use the wave i.e. speed of sound as 1480m/s. a. What frequency will be reflected off the enemy? b. What frequency will be received by your submarine from the reflection? c. The enemy stops and sends his own signal of 600.0Hz. You receive his signal at what frequency? You are still moving towards him.

Answer 1

a)
If the initial source ( your submarine ) and the receiver (your enemy ) are moving toward each other , then, the Doppler shifted frequency received by the receiver of the enemy and reflected back
   
where, c = 1480 m/s, is the speed of the sound, ,  is the speed of the receiver ( your enemy ) and ,  is the speed of the source ( your submarine ).
And given the original frequency of the sound   , we get the frequency of the reflected sound from the enemy


  

b)

Now when the sound is reflected off the enemy, the source of the sound now becomes the enemy and the receiver now becomes you. The sound will again be Doppler shifted because of your motion when you receive the sound, so, the frequency of the sound received by you is
   

And so, we have the received frequency by you,
  
  

c)
  In the case when the enemy stops and sends signal of frequency , then the sound received by you is
  
And putting the given values, i.e, , , we get