31
Dec
Energy Stored In Standing Wave. I think this is what is meant by energy being stored in a standing wave. The total energy density in a harmonic wave on a stretched string is given by frac12p A2 omega2 sin2kx-omega t We can see that this energy oscillates between a maximum and a minimum. Energy will flow into the string causing the standing wave to form at a later time. Therefore there is energy stored in the string.
It has energy but this feature of a standing wave contains the energy appearing as stored energy. Because When energy is moving right to left red it the energy is propagating through the medium. The total energy density in a harmonic wave on a stretched string is given by frac12p A2 omega2 sin2kx-omega t We can see that this energy oscillates between a maximum and a minimum. Assume that there is no energy loss in the process of either transfer or reflection of the waves. Once they start interfering there is zero net propagation of this energy through the system. This happens as energy is transformed from potential or stored energy to kinetic or movement energy and then back to potential energy again.
The bottom line is that the standing wave when viewed as an interference pattern clearly just redistributes the energy of the two traveling waves which themselves distribute the energy uniformly taking energy away from some regions of the medium and giving it to others.
Lets say that this is an ideal model motivated by a string as a medium with both ends closed. In this paper we optimized the design of a standing wave. Although the string is straight at time parts of the string have nonzero velocity. Learn more about standing waves. So the energy is maximum at 0 displacement when the string is stretched and at its maximum speed both KE and PE density are maximum at the same time and minimum when the displacement is maximum as. The kinetic energy K 1 2 mv 2 of each mass element of the string of length Δ x is Δ K 1 2 Δ mv y2 as the mass element oscillates perpendicular to the direction of the motion of the wave.