Homework Help: How do you find the phase difference when given two sine equations and a X and t

1. Jan 26, 2013

randoreds

ok, I would just like to know in general b/c we have to do this a lot.
The equations have the same amplitude, but different k and w
suppose you have y1 = Asin(k1x-w1t) and y2 = Asin(k2-w2t)

and only other information is they are on a string, at a point x, and a time t.

side note anyone know any good websites for help with superposition and standing waves b/c this section I am struggling with : /

2. Jan 26, 2013

haruspex

If the frequencies are different then the phase difference will also vary with position and time. Your two equations are not quite general, They assume the waves are in phase at x=0, t=0. So let's expand them to sin(kix+wit+ci).
At a given x and t, the phases are kix+wit+ci. So the phase difference is simply the difference of those two quantities (but you probably want to reduce that modulo 2π).

3. Jan 26, 2013

randoreds

Thanks for the help. but I still have a question, What do you mean by ci? b/c I thought I could get the answer by subtracting the difference of the two -> kix+wi , but I get totally the wrong answer. I get 9 radians and the answer is 152 degrees. So I would suppose that variable ci is what I am missing. so if you could explain it, I would be grateful!

and I suppose c is the phase constant, but how would you solve for it in this situation

Last edited: Jan 26, 2013
4. Jan 26, 2013

haruspex

As I said:

5. Jan 26, 2013

randoreds

sorry, im terrible at physics. I get 20(5) -32(2) = 36, 25(5) - 40(2) = 45, 45 - 36 = 9 radians if you convert that to degrees, pi/20.

therefore, I have no idea how to get to the answer from there. any n2pi wont give me 152 radians. I get like 171 or 351.

It might be simple, but how do you get from my answer to the right one?

6. Jan 26, 2013

haruspex

To convert radians to degrees, multiply by 180/pi.

7. Jan 26, 2013

randoreds

oh, I can't believe I was making that mistake. thank you so much.

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