Question

A transverse wave on a string has an amplitude A. A tiny spot on the string is colored red. As one cycle of the wave passes by, what is the total distance traveled by the red spot?

a.) 4A
b.) 1/2 A
c.) 1/4 A
d.) A
e.) 2A

Answer 1

The total distance traveled by the red spot as one cycle of the transverse wave passes by is 4A.

Step-by-step explanation:

The total distance traveled by the red spot as one cycle of the transverse wave passes by is 4A.

To understand why, it helps to think about how the wave moves. In a transverse wave, the particles of the medium oscillate perpendicular to the direction of wave propagation. This means that as the wave moves forward, each individual particle moves up and down.

During one complete cycle of the wave, the red spot on the string will go through one complete oscillation, which consists of both an upward displacement and a downward displacement. So, it will travel a distance equal to twice the amplitude, which is 2A, both upwards and downwards in total. Therefore, the total distance traveled by the red spot is 2A + 2A = 4A.

Answer 2

Answer: E. 2A

Step-by-step explanation:

Amplitude(A) of a wave is the displacement of a body from its position of rest. The maximum value of the amplitude is the crest and the minimum value is the trough.

For a wave to make a cycle, it has to move to and from from its point of displacement.

If the red spot on the string completes a cycle, this means it must have pass through the crest and the trough making it 2 amplitudes.