# Doppler Effect Submarine Problem

mjsd
Homework Helper
Choosing a reference frame so that sub 2 is stationary and sub 1 is moving at 17 m/s is a bad move. You get close to the right answer though because the speeds of the subs are very small compared to the speed of the waves. Consider this same system where the speed of the wave is lets say, 100 m/s and you'll see what I mean. Using you're method, you'll get the frequency detected by sub 2 as 1638 Hz as opposed to 1811 Hz using the Doppler method. This should clear up what you're talking about in the second paragraph of you're response too.
Finally, the objective of this thread is to gain some authority with which to challenge my professor who marked my answer of 1423 Hz as incorrect on my midtem exam. ???

I know this thread has been marked "solved". But I just want to make one comment. It doesn't matter which frame you choose to do your calculations, the answer will be exactly the same. If you want to avoid rounding errors, keep everything in fractions.

Doc Al
Mentor
I know this thread has been marked "solved". But I just want to make one comment. It doesn't matter which frame you choose to do your calculations, the answer will be exactly the same. If you want to avoid rounding errors, keep everything in fractions.
As madchemist pointed out in post #21, choosing a frame of one of the subs only works if the speeds are small with respect to the speed of sound.

$$\frac{V + V_o}{V - V_s} = \frac{1 + V_o/V}{1 - V_s/V}$$

As long as $V_o/V << 1$ & $V_s/V << 1$:

$$\frac{1 + V_o/V}{1 - V_s/V} \approx (1 + V_o/V)(1 + V_s/V) \approx 1 + V_o/V + V_s/V = \frac{V + V_o + V_s}{V}$$

But this is just an approximation; not bad in this case, but it falls apart when the speeds of the subs are significant.

In any case, when using the Doppler formula you are implicitly using the frame of the water, since that's the medium through which the sound travels.

mjsd
Homework Helper
As madchemist pointed out in post #21, choosing a frame of one of the subs only works if the speeds are small with respect to the speed of sound.

you really missed the point I was trying to make, namely, physics is the same no matter which frame you use and you get the right answer. in this case, we know that the formulas as they are are written down w.r.t. the frame of the medium in which the sound waves travel. So, if you use the frame of the sub, you just need to take that into account ie. water is moving w.r.t. sub so the formula would change slightly. But as you said in this case, since speed of sound is >> speed of sub, it doesn't really matter.

Doc Al
Mentor
you really missed the point I was trying to make, namely, physics is the same no matter which frame you use and you get the right answer. in this case, we know that the formulas as they are are written down w.r.t. the frame of the medium in which the sound waves travel. So, if you use the frame of the sub, you just need to take that into account ie. water is moving w.r.t. sub so the formula would change slightly. But as you said in this case, since speed of sound is >> speed of sub, it doesn't really matter.
And you really missed the point that I was trying to make, namely, that your analysis is incorrect.

Done properly, a change in frame gives you the exact same answer, not just one approximately the same. The fact that your formula only works approximately should tell you that something is wrong.

mjsd
Homework Helper
sorry, not following you here. must have been me making typos here and there and not careful with my English or whatever.... But I firmly believe that I did no wrong when I got 1431 Hz for the answer although I didn't show my actually workings here. Since this thread is supposedly closed, I should say no more.

Doc Al
Mentor
But I firmly believe that I did no wrong when I got 1431 Hz for the answer although I didn't show my actually workings here.
Perhaps I've misinterpreted what you've been saying. Only one way to find out: Show your work and let's take a look. Up to you.