How Deep is the Ocean Using Ultrasonic Waves?

[smillphysics]

A sonar generator on a ship produces periodic ultrasonic waves at a frequency of 2.3 MHz. The wavelength of the waves in sea water is 4.9 · 10-4 m. When the generator is directed downward, an echo is received 16.2 s later. How deep is the ocean in m?

Frequency=1/T
Velocity=wavelength/T= frequency * wavelength
Wave motion towards +x y=Asin (2*pi*frequency*time-2*pi*x/wavelength)

This echo goes down in and hits the ocean floor and then comes back up. The distance may be multipled by 2.
I want to use the wave motion but A is not given and none of my formulas help me solve for A. so I would say y=Asin *(plug in everything except for x?) And try to solve for x but I have no idea how I go about this. Any help?

 

[berkeman]

A sonar generator on a ship produces periodic ultrasonic waves at a frequency of 2.3 MHz. The wavelength of the waves in sea water is 4.9 · 10-4 m. When the generator is directed downward, an echo is received 16.2 s later. How deep is the ocean in m?

Frequency=1/T
Velocity=wavelength/T= frequency * wavelength
Wave motion towards +x y=Asin (2*pi*frequency*time-2*pi*x/wavelength)

This echo goes down in and hits the ocean floor and then comes back up. The distance may be multipled by 2.
I want to use the wave motion but A is not given and none of my formulas help me solve for A. so I would say y=Asin *(plug in everything except for x?) And try to solve for x but I have no idea how I go about this. Any help?

You need the propagation velocity of sound in seawater. Is that not given in the problem statement? If not, you can use Google to look it up.

 

[smillphysics]

I actually can't find the velocity of sound is sea water. The problem only gives the information listed above. Any other suggestions on how to solve this problem?

 

[berkeman]

I actually can't find the velocity of sound is sea water. The problem only gives the information listed above. Any other suggestions on how to solve this problem?

As I said in my post, if the problem does not state if for you, use the web search engines to figure it out. I initially used Google, but one of the first best hits was at wikipedia.org, so maybe I should have just started there. Go to wikipedia.org, and search on speed of sound in seawater. There is a very helpful graph there, which will give you the speed of sound in seawater versus depth.

First, figure out what a good average approximation is for the speed of sound at all depths, and calculate the answer to your problem. Then using that answer, re-calculate a better answer, taking into account that the speed of sound varies with depth (as shown in the wikipedia graph).

What do you get for the approximate depth answer. What about the refined depth answer?