Reflection of Sound | Reflection of Waves
Reflection of Sound | Reflection of Waves :- In this article, we are going to study about the reflection of waves (transverse and longitudinal) at the boundary of the denser medium and rarer medium. When a wave travelling in a homogeneous medium strikes an interface separating two media, a part of incident wave is reflected back into the first medium while the remainder is partly absorbed and partly refracted(or transmitted) into the second medium. Both light waves (transverse waves) and sound waves (longitudinal waves) exhibit this phenomenon. As the wavelength of a light wave is very very small of order 10-10 m, hence it can be reflected from a small surface. While the wavelength of a sound wave is large of order 10-3 m, hence it requires a large surface for reflection.
(1) Reflection of Transverse Waves From Denser Medium
(Reflection of Sound | Reflection of Waves)
When the pulse reaches the right end which is clamped at the wall [Fig (b)], the leading edge of the pulse exerts a force on the wall and the wall exerts equal and opposite force on the element(According to Newton’s Third Law). Now as the wall is rigid, it cannot move but the reaction force on the rope by the wall produces a pulse that is inverted but identical to the original pulse [Fig (d)]. The result of this change is that the pulse undergoes reflection— that is, the pulse moves back along the string in the opposite direction [Fig (e)].
Thus after reflection at a denser medium, a crest returns as a trough i.e. there is a phase change of π radian or 180° between the incident wave and the reflected wave.
Incident wave (Travelling along + x-axis) :-
Reflected wave (Travelling along – x-axis) :-
Here A’ < A, because of the energy loss and a phase change of π – radian, because of the reflection from rigid boundary.
(2) Reflection of Transverse Waves From Rarer Medium
(Reflection of Sound | Reflection of Waves)
The right end of the string is attached to a light frictionless ring which can freely move on a vertical rod. A wave pulse is sent on the string from left. When the wave pulse reaches the right end, the ring at this end is acted on by the force to go up. As the ring is free to slide along the rod, it is displaced in upward direction more than the height of the pulse i.e., it overshoots the normal maximum displacement [Fig (b)]. At this position the ring and string come momentary to rest. But since the string is stretched in this position, so the free end of the string is pulled back down and again an extra force acts from right which sends a wave from right to left with its shape identical to the original one [Fig (c)]. Thus, a wave is reflected by the free end (rarer medium) without inversion.
Thus after reflection at a rarer medium, a crest returns as a crest i.e. there is a no phase difference between the incident wave and the reflected wave.
Incident wave (Travelling along + x-axis) :-
Reflected wave (Travelling along – x-axis) :-
Here A’ < A, because of the energy loss.
(3) Reflection of Longitudinal Waves From Denser Medium
(Reflection of Sound | Reflection of Waves)
Assume that longitudinal waves in air (sound waves) are incident normally on a rigid wall. As the compression strikes the wall, it applies a force on the wall. But since the wall is rigid, it exerts an equal and opposite force on the layer of air in compression and thus pushes the compression in the backward direction. There is a phase difference of π radian or 180° between the incident wave and the reflected wave. This is because the displacement of the particles of the medium in the reflected wave is in the opposite direction to the displacement of the particle in incident wave.
Thus a compression travelling towards the right is reflected as a compression travelling towards the left. Similarly, incident rarefaction is reflected as a rarefaction and hence nature of the wave remains the same i.e., incident and reflected waves looks similar.
(4) Reflection of Longitudinal Waves From Rarer Medium
(Reflection of Sound | Reflection of Waves)
Assume that a longitudinal wave travelling in a denser medium is incident at the Interface (boundary) of a rarer medium. As the compression in the incident wave strikes the interface (e.g. air at the open end of a pipe) then due to the high pressure of compression, the interface is pushed back towards the rarer medium. This creates a low pressure region because the surrounding air goes away quickly and compression is converted into a rarefaction before the wave is reflected.
Thus, the compression after reflection at a rarer medium returns as a rarefaction and similarly, incident rarefaction is reflected as a compression. Thus no phase change takes place when a longitudinal wave is reflected from the surface of a rarer medium but the nature of the wave is changed i.e., incident and reflected waves looks different.
