Question

in the lecture of energy in waves of professor lewin
he concluded the lecture with a question about amplitude of the transmitted pulse in a string with an open end ,the formula gave the amplitude of transmitted pulse as twice of the incident pulse
so how does it go with conservation of energy ?

Answer 1

The reflected wave is lower than the incident wave and the transmitted wave is on a lighter string. The sum of their energies should be equal to the energy of the incident wave.

Answer 2

it was string with free end ,like string attached with a massless ring , the formula for amplitude of transmitted wave shows some amplitude but there is no second string on which transmitted wave can go

Answer 3

Just as an unterminated transmission line or a transmission line terminated in an impedance different than its' characteristic impedance, there will be a reflected wave which when combined with the incident wave creating "standing waves" There will be points where the amplitudes combine additively and points where they will combine subtractively, but in all cases the law of conservation of energy is preserved.

Answer 4

hmm , maybe my question was not clear in the first place
amplitude of transmitted wave /amplitude of incident wave =2*v(2)/(v(1)+v(2)
where v(1) and v(2) are velocities in medium 1 and medium 2
now if refractive index of medium two is 0 ,that is for string attached with a massless ring
v(2) is infinite and we get the amplitude ratio as 2,but there is no string on the other side of massless ring
how is this explained

Answer 5

Sorry, I didn't understand the "refractive" element part of the question.

Answer 6

if there is no string ,we can consider a string with refractive index 0

Answer 7

Any point of the string, reached by the wave, will be displaced according to elastic forces (to the left and to the right of the point) trying to restore it to its original position.
All points are the same with this respect and will show, in turn, a pulse of the same height EXCEPT the one at the end which feels the elasticity of the string only on ONE side. This is why it will react with a double amplitude.
There is no 'magical' energy created here.