Question

When a string is vibrating in a standing wave pattern the power transmitted across an antinode, compared to the power transmitted across a node, is:

A) more

B) less

C) the same (zero)

D) the same (non-zero)

E) sometimes more, sometimes less, and sometimes the same

The answer is C, Could anyone explain it?

Answer 1

The standing wave is a stationary wave

A particle of the string at a node, however, experiences no displacement. Thus, it cannot do work on the neighboring segment. As a result, no energy is transmitted along the string across a node, and energy does not propagate in a standing wave. For this reason, standing waves are often called stationary waves.A standing wave consists of an alternating pattern of nodes and antinodes. When a standing wave pattern is established in a medium, the nodes and the antinodes are always located at the same position along the medium. Ther is no change in the position of the particle like the travelling wave. Hence the work done is zero and hence the power transmitted across the point of nodes & anti nodes is zero.