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

[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 : /

 

[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(k_ix+w_it+c_i).
At a given x and t, the phases are k_ix+w_it+c_i. So the phase difference is simply the difference of those two quantities (but you probably want to reduce that modulo 2π).

 

[randoreds]

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(k_ix+w_it+c_i).
At a given x and t, the phases are k_ix+w_it+c_i. So the phase difference is simply the difference of those two quantities (but you probably want to reduce that modulo 2π).

Thanks for the help. but I still have a question, What do you mean by c<sub>i? 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</sub>

 

[haruspex]

I get 9 radians and the answer is 152 degrees.

As I said:

(but you probably want to reduce that modulo 2π)

 

[randoreds]

sorry, I am 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 won't 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?

 

[haruspex]

9 radians if you convert that to degrees, pi/20.

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

 

[randoreds]

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