Doppler effect of submarines question. Please help

[XxDonniexX]

Homework Statement

A French and a U.S. submarine are moving directly towards each other during manoeuvres in still water. The French submarine is moving at 50.0 km.hr-1. It sends out a sonar signal at 1100.0 Hz. The frequency detected by the French submarine (reflected back from the U.S. submarine) is 1222 Hz. How fast is the U.S. submarine traveling towards the French submarine? Assume the velocity of sound in sea water is 1500 ms-1.

Homework Equations

The Attempt at a Solution

I tried making one up lol. f`= f / ((1-(v_F + v_US)/v)
Where v_F is the velocity of French and v_US is american, v is speed of sonar signal, f = frequency of sonar signal, so i rearranged to find v_US but I am 100% sure this is not the way to do it.

 

[cartonn30gel]

If you just want to solve the problem, look up the equation from a textbook or a website. If you want to understand why that equation works (no the one you wrote) try drawing a picture and consider when two consecutively sent wavefronts are received back at the French ship. If you do that, you will actually end up proving the non-relativistic Doppler shift equation.

Note: That equation you wrote is confusing. Also you shouldn't just add the velocities like that; that's not what you want. It's for you to figure out why.

 

[XxDonniexX]

I know the equation i wrote is not right, the answer i got for the US sub is 135.86 m/s. Thats wayyy too fast. Thats why i need help, what is the right equation?

 

[XxDonniexX]

ok i got a new answer. The speed of the US sub is 68.52 m/s. This still seems pretty fast compare to the French sub but i think it's right, i was told that the velocity of the US will be quite large. Can someone see if your answer agrees to mine please.

 

[EzaMoo]

I am stumped on this as well...

towards the us sub I have

f = (1500 +Vus / 1500 - 50) x 1100

Then back to french I have

1222 = (1500 +50 / 1500 - Vus) f

But I assume this is incorrect because when I sub the first into the second Vus cancels out...

 

[XxDonniexX]

hmm well i tried doing it another way.
the difference frequency between when the french sub gives out and receives back is 122 Hz. So that means I am assuming that the US sub would receive half that frequency, therefore rebounding an extra 61 hz plus the 1100Hz. Then just using that formula once to find V_us.
Still not sure if it would be ok to do that though

 

[EzaMoo]

I finally got it! need to take f' of both those equations then sub them. Works out to around 65m/s

 

[pat666]

its meant to be fricken fast your 68m.s is right