proof of Phase change

[l3010o]

how can we proof the phase change from denser spring to a less dense one?

[Mentz114]

Do you mean 'prove' ? Please explain the problem more. Is this in relation to a simple harmonic oscillator ?

[l3010o]

i mean how to prove these?
http://www.kettering.edu/~drussell/Demos/reflect/reflect.html

[billiards]

Do you mean phase changes in the earth which cause seismic reflections?

[l3010o]

i think that's not related to the seismic reflection.

I want to know if there is any proofs of

"how do the wave speeds compare for the two strings?
From high speed to low speed (low density to high density)"
located at
http://www.kettering.edu/~drussell/Demos/reflect/reflect.html

[AlephZero]

You write expressions for the waves at the interface (incident, reflected and transmitted) with unknown phases, and use the boundary conditions to find the relation between the different phases.

I don't have a reference off hand, but most textbooks on acoustics, vibration transmission, etc. should work through details of the maths.

[l3010o]

can it be proved by momentum?
i can find them in the textbooks, but without the proofs