How does energy transmission work in waves?

[Owen-]

After looking at my notes and http://cnx.org/content/m16027/latest/" I have become utterly confused about Energy transmission in Waves.

Since the expression of elastic potential energy is same as that of kinetic energy

What? In a traveling wave KE=PE?

If so, when a particle is at its max displacement, KE=PE=0 and so KE+PE=0
and yet then a particle is as its mean position KE=PE= constant >0

How is this possible? KE+PE is total energy, shouldn't this be constant? I.e. when KE increases PE decreases but total energy remains the same?

Apologies if this is a stupid question :P
Owen.

 

[Bill_K]

Depends on what kind of wave you're talking about. The kinetic energy plus the potential energy at a point is the energy density at that point. Energy conservation says that this energy density will remain constant as it travels along with the wave. It does not say that the energy density is the same at all points within the wave. For example for an electromagnetic wave there will be places where E = B = 0, and here the energy density is zero. At other places E and B are both max. That's why we take care to speak about the average energy density.

 

[Owen-]

Ah ok thanks :) Just let me confirm - in a traveling wave the energy traveling in the y direction varies, but the energy transmitted along the x-axis remains constant? :s

 

[chrisbaird]

It sounds like you are talking about waves on a string. In that case, potential energy does not always equal kinetic energy. When a part of the string is at its maximum displacement, it is momentarily at rest and therefore has no kinetic energy. All of its energy is potential. When that part of the string reaches the midpoint of its swing, it is at its maximum speed so all of its potential energy has been converted to kinetic energy. The total energy is constant so PE and KE trade off back and forth as the wave oscillates. Think of it like a pendulum.

 

[Bill_K]

Except it is not like a pendulum. Waves on a string behave the same way as described above for electromagnetic waves. When a part of the string is at its maximum displacement, it has no kinetic energy and no potential energy. When a part of the string reaches the midpoint of its swing, it has both maximum kinetic energy and maximum potential energy. The energy travels along the string. It is maximum at some places and zero at others, but does not remain constant at a particular point.