Question

The drawing shows a snapshot of a transverse wave moving to the left on a string. The wave speed is 10.0 m/s. At the instant the snapshot is taken, 

(a) In what direction is point A moving? 

(b) In what direction is point B moving? 

(c) At which of these points is the speed of the string segment (not the wave speed) larger? Explain. 

(d) How do your answers change if the wave moves to the right instead?

Answer 1

Strategy:

When a transverse wave flows in a medium, the particles in medium oscillate back and forth about their mean position as the wave’s passes. The direction of oscillation is perpendicular to the direction of wave propagation.

 

Solution:

Given:

Speed of wave, v = 10.0 m/s

 

On the assumption that the wave is a transverse wave:

Whenever a transverse wave propagates in string, the particles of string vibrate up and down. This happens till there is wave energy at that point and after the wave goes away, the point again comes to its initial position.

 

a)

In the figure shown above, the wave is moving from right to left with a speed 10.0 m/s, but the points on string vibrate up and down. Therefore, point A on the string moves upward for the figure shown.

 

b)

For the figure shown, point B is moving downward to its initial position (position of point B when there was no wave).

 

c)

The velocity at point A will be greater than point B. This is so because the slope of the forward portion (seen from left) of wave is more than the backward portion (seen from left). Hence, point A will have to travel quickly to reach the amplitude of wave. Point B, on the other hand, lies in the backward portion, which has a lower slope, and thus provides sufficient time for B to reach its initial position.

d)

For the wave moving towards right, point B will fall into the forward portion of wave and will move fast to reach the wave amplitude, whereas, point A will get enough time to reach back at its initial position. The figure for this scenario is shown below.