Question

The speed of sound in seawater is approximately 1480 m/s. You are at a depth of 50.0m a. You ping the ocean bottom and receive the echo back 0.125 seconds later. How deep is the ocean at this point? b. If the frequency of the sound is 500.0 Hz, what is the wavelength of the sound? c. The ping coming back to the submarine has an intensity of as -80.0 dB. What is the intensity of the returning sound wave? d. Use the distance in part (b) and the answer in (c) to find the power of the reflected sound.

Answer 1

a)
Let the depth of the ocean be H. Then the time required for the sound to travel from the observer to the bottom of the ocean and come back to the observer is given by
  
  
Now putting the given values,
  v = 1480 m/s, t = 0.125 sec,
we get the depth of the ocean at that point
   
  
This is the distance of the bottom of the ocean from the observer which is itself h = 50 m down the water. So, the depth of the ocean from the surface of the water is
   

b)

The frequency of the sound is given by
   
And so, the wavelength of the sound is
  

c)

According to the definition of the decibel,
  
where,
    is the reference level for the intensity. And so, for the given value,
  , we have
  
  
   
   
   
  
This is the intensity of the returning wave.

d)

The power of the sound is
  
So, for r = H = 92.5 m, we have