Conceptual question about longitudinal waves

Saladsamurai

So we are working on sound waves in my physics course now and I was doing some textbook reading. I have been following it pretty well, but I just came across a relationship that I am not quite following.

It is with reference to wave interference. Let us say that two sound waves are emitted from two different point sources [tex]S_1[/tex] and [tex]S_2[/tex]. The waves have the same wavelength [tex]\lambda[/tex] and are in phase at their sources. They take paths of lengths [tex]L_1[/tex] and [tex]L_2[/tex] and pass through point P.

The text says that their phase difference [tex]\phi[/tex] is dependent on [tex]\Delta L=|L_1-L_2|[/tex]

Thus to relate the variables [tex]\Delta L[/tex] and [tex]\phi[/tex] we can use the proportion: [tex]\frac{\phi}{2\pi}=\frac{\Delta L}{\lambda}[/tex]

I know that I should see it, but I don't exactly follow this proportion.

Could somebody ellaborate on this a little for me? I sure would appreciate,
Casey

learningphysics

Suppose the equation of both waves is: y = Acos(kx) (going along the direction the wave is travelling)

The wavelength of this wave is 2*pi/k

So at the point of interest, suppose wave 1 has travelled L1, and wave 2 has travelled L2:

y1 = Acos(kL1)

y2 = Acos(kL2)

the phase of the first wave is kL1. the phase of the second is kL2.

phase difference is: kL1 - kL2 = [2*pi/wavelength]*(L1 - L2)

so from this we get the phase difference relationship.

Saladsamurai

Ah. I see that now. Thanks LP. It makes even more sense now that I wrote out what you did^^^...the phase difference is [tex]\phi[/tex]

Casey