A wave pulse moves along a stretched rope in the direction shown. Which diagram correctly shows the variation with time t of the displacement s of the particle P in the rope?

Question 16

A wave pulse moves along a stretched rope in the direction shown.

Which diagram correctly shows the variation with time t of the displacement s of the particle P in the rope?

Reference: Past Exam Paper – June 2015 Paper 13 Q26 & March 2018 Paper 12 Q21

Solution:

Answer: D.

Particular care is needed with this type of question, which requires interpretation of graphs.

Remember that the wave formed is a transverse wave – the direction of vibration (of the particles on the rope) is perpendicular to the direction of propagation (which is to the right, as indicated by the arrow).

The particles can only vibrate vertically – that is, they move up and down. Thus, particle P will only move up and down, it is not moving horizontally.

Consider the wave some instant later.

This is done by displacing the waveform slightly to the right (since the wave is moving to the right).

After some time, the vertical part (on the right) will be at P – particle would move according to the form of the wave.

So, at the earliest time there is a sudden jump up, followed by a constant high value of displacement s and finishing with the negative peak.

The answer is therefore D.

 

Note that s is the displacement. Positive values of s means that P has moved upwards and negative values correspond to its downward movement.