Racking my brains over this :
If I have two semi-infinite strings (made of same material) - which are connected by a massless spring, and now I send a longitudinal wave along one string.
Will the spring just pass on the wave to the other string or will it serve to reflect some of it back ?
If it does reflect some of it back, what would be the boundary conditions that you will have to impose ?
Is it just that the E * du/dx which is the stress in the two strings, should be equal to k*(u1 - u2) where u1 and u2 are the displacements of the two strings at the interface between the string and the spring ? So I will just have:
E * du1 /dx = -k * (u1 - u2)
E * du2 /dx = k * (u1 - u2)
One of the right hand sides is of opposite sign as the direction of force is opposite.
Not able to show energy conservation with this. Perhaps I am using the wrong boundary conditions ?