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Reflection of Waves

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Reflection of Waves - Lesson Summary

If the boundary is not completely rigid or if it is an interface between two different elastic media a part of the wave is reflected and a part is transmitted into the second medium.
 
Reflection of waves follows the Laws of Reflection, which are similar to the Laws of Reflection of Light.
 
To understand the phenomenon of reflection of waves, we can perform two simple activities.
In the first activity, the left end of a string is fixed to a rigid wall.
 
In the second activity, the left end of the string is tied to a ring which can slide up and down without any friction, on a rod.
 
A single pulse is generated at the free end of the strings.
 
In the case of the first activity the pulse, on reaching the left end of the string encounters the rigid wall.
 
The pulse applies an upward pull on the wall and the wall applies an equal but opposite downward pull on the string obeying Newton’s Third Law of Motion. The downward pull by the wall on the string generates a pulse which travels in a direction opposite to that of the incident pulse.
 
As there is no displacement of the particle at the junction of the string and the wall the incident and reflected pulses have opposite signs and cancel each other at that point. Due to this phenomenon, the reflected pulse has a phase reversal or a phase difference of pie or 180 degrees.
 
In the second activity when the pulse reaches the end of the string it pulls the ring up.
As the ring moves up it pulls the string, producing a reflected pulse with the same sign and amplitude as the incident pulse.
 
In this process, the incident and reflected pulses reinforce each other, creating maximum displacement at the end of the string.
 
The reflection is without any additional phase shift.
 
Let us now express these observations mathematically.
The incident wave is represented by
 
, where ‘a’ is the amplitude and ‘k’ is the wave number of the wave
 
The reflected wave from a rigid boundary is represented by
 
 
For the reflection at an open boundary the reflected wave is represent by

 
When a wave is incident obliquely on the boundary between two different media we know that a part of it is reflected and a part is transmitted to the second medium.
This transmitted wave is called the refracted wave.
Refraction of waves follows Snell’s Laws of Refraction as in the case of a beam of light.

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