Question

A long string is stretched and its left end is oscillated upward and downward. Two points on the string are labeled A and B.
At the instant shown, orient v(A) and v(B) to correctly represent the direction of the wave velocity at points A and B.
At each of the points A and B, rotate the given vector to indicate the direction of the wave velocity.

Answer 1

Concepts and reason

The concepts required to solve this question are the wave velocity and the phase velocity.

Initially, differentiate between the wave velocity and the particle velocity and using the definition of the wave velocity, draw the direction of the wave velocity at points A and B. Then, find the velocity from the diagram given in the question and find the change in position at point A and point B. Finally, using the position of point A and point B, draw the direction of the velocity.

Fundamentals

The wave velocity is defined as the velocity at which the wave crests or any other part of the wave progress through the medium.

The particle velocity is defined as the velocity of the particle in a medium when the particle transmits a wave.

(A)

The wave velocity is the velocity with which the wave travels in space.

In a transverse wave, the wave velocity and the particle velocities are perpendicular to each other.

When a string is stretched, the wave will travel away from the source of the wave along the length of the string and this will be represented by the following figure:

(B)

The wave travels through the string in this case. The velocity of the individual particle on the string is different from the velocity of the wave as it passes through the string. It can be viewed that the left end of the string is the source of wave disturbance.

The left end is the source of the wave. The wave crest to the immediate left of the point A will raise the position of the point A. Similarly, depending in the location of the source of wave, the wave trough will lower the position of the point B. This can be represented by the following figure:

Ans: Part A

The orientation of two vectors is:

Part B

The orientation of two vectors is: