A longitudinal wave has vibrations parallel to the direction of transfer of energy by the wave.

Q#17 (Past Exam Paper – June 2018 Paper 11 Q22)

A longitudinal wave has vibrations parallel to the direction of transfer of energy by the wave.

The wave can be represented on a graph showing the variation of the displacement of the particles with distance from the source.

Which point on the graph is the centre of a compression?

Solution:

Answer: B. 

The graph shows how the displacement of particles vary with distance from the source.

Points A, B, C and D are at specific distances from the source.

From the y-axis, the particles move away from the source when they have a positive value and they move towards the source when they have a negative value.

For a longitudinal wave, the direction of vibration is parallel to the direction of transfer of energy by the wave.

A compression occurs when the particles are close to each other. Let the centre of compression be X. If particles on the left of point X are moving towards the right (towards X), then particles on the right of point X would be moving towards the left (again, towards X). So, particles on each side of the centre of compression (X) are moving towards each other (and towards X).

From distance = 0 towards point A, the particles move away from the source as the displacement is positive.

From point A towards B, the displacement is still positive. So, the particles are still moving away from the source.

So, just before point B the particle is moving away from the source (towards B) as the displacement is positive, and just after point B it is moving towards the source (as the displacement is now negative) and also towards B (as the particle is returning on its path towards the source).

So, B must be the centre of a compression.

Point D is the centre of a rarefaction as just before D, the particles are moving towards the source (and away from D) since the displacement is negative. And just after D, the particles are moving away from the source (and away from D) since the displacement is now positive. So, the particles are moving away from each other and D is at the centre. This is rarefaction.

The other two points are midway between centres of compression and rarefaction.