How Do You Determine Sound Intensity and Speed of an Enemy Submarine?

[biomajor009]

Homework Statement

You are the captain of a submarine that is on a secret mission deep inside enemy waters. Suddenly your ship is “pinged” by another sub. You are able to determine that the ping comes from the North, has an intensity level of 86.4 dB, and has a frequency of 7270 Hz. You know that the standard ping on an enemy sub has an apparent frequency of 7230 Hz and emits 990 Watts of power. At the instant you get pinged your sub is moving Northward at 14.3 m/s. Note: the speed of sound in sea water is 1530 m/s.
(a) What is the intensity of the ping you hear?
(b) How long did it take the “ping” to travel from the enemy sub to your sub?
(c) How fast is the enemy sub moving? Are they moving toward you or away from you?
(d) You take evasive action and head South to get make sure you get as far as possible from the enemy sub. You are exactly are two kilometers away from the enemy sub when you hear the next ping. What is the intensity level of the ping that you hear this time?

Homework Equations

The Attempt at a Solution

I found the intensity in (a) to be 4.37 * 10^-4
Then I found the time it took in (b) to be 0.278 seconds
I know that in (c) it should be moving toward you, but I don't know how to figure out the source's speed. What equation should I be using?
Then for (d) I found the new intensity level to be 72.94dB

 

[Saladsamurai]

I believe you need to use the apparent frequency equation $$f'=\frac{v\pm v_D}{v\pm v_s}f$$

where f' if the apparent frequency; f is the real frequency;v_s is speed of source; v_d is speed of detector; v is the speed of sound through that particular medium.

You need to make commen sense assumptions as to whether to use + or -. For example if f' is higher than f then their are some different possiblities. What would making the numerator/denominator bigger/smaller do to the overal value of the fraction (that is in fact f')?

Casey