Question

Q2;a string of tension T and mass per unit length M propagates waves. Let the amplitude of waves be A .
a)Try to reason , using the idea that a standing wave results from two traveling waves , that the kinetic energy and the potential energy in traveling waves are equal.
b)what is the kinetic and potential energy per unit length of the string?

Answer 1

i know the answer for part a)
a standing wave is formed due to the interference of similar waves travelling in opposite direction.
these waves should be similar as follows:
the waves should have the same amplitude
same frequncy
same velocity
their phase need not to be the same
as the wave velocity , amplitude, frequncy are equal, the potential and kinetic energies would be equal
as these quantities are same in both the waves the potential energy and the kinetic energy would be the same as these re determined by the above factors
the K.E. and the P.E. are also determined by the factors such as mass per unit length and the tension but we consider the velocities of the waves to be equal , these parts get countered
i hope this helped you:)

Answer 2

"a)Try to reason , using the idea that a standing wave results from two traveling waves , that the kinetic energy and the potential energy in traveling waves are equal."

Standing waves are formed by two (identical) propagating waves traveling in opposite directions. If the waves have different characteristics, we'll get a combination of standing and propagating waves.

As for the reasoning. propagation of wave can be understood in terms of propagation of energy.

For a standing wave, the (net) movement of energy across any cross-section (over the time period) is zero; hence the two (initial) traveling waves must be equivalent in terms of energy.

"b)what is the kinetic and potential energy per unit length of the string?"
Simply add the respective energies (per unit length) of the two traveling waves. (Why?)

Answer 3

what is Formula of potetial energy?

Answer 4

1/2 kx^2

Answer 5

where k is the spring constant and x is the extention in the spring over it's natural length

Answer 6

and work that you have to do become the potential energy?

Answer 7

can you prove up formula?

Answer 8

@rajat97 ,@LastDayWork can help?

Answer 9

@fazeli
I'll strongly advice you to refer to your book for the proof. You may ask your doubts about it..here

Answer 10

it comes up from the work energy theorem and energy conservation