Question 17
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?
Reference: Past Exam Paper – June 2018 Paper 11 Q22
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.
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