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Reflection of waves is the sudden change in the propagation of waves after colliding the interphase of the two distinct mediums. An example of the reflection of waves can be the skipping of ropes. The movement which is possessed during skipping ropes is due to the standing waves. Another such example is the phenomenon of echo. It occurs when the sound comes back due to the reflection of waves for distant objects and comes back to the listener after a little delay.
Read Also: Relation between Frequency and Velocity
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Key Terms: Reflection, Waves, Rays, Reflection of Waves, Incident Ray, Inelastic Collision, Refracted Ray, Fixed End Reflection, Free End Reflection
What is the Reflection of the Waves?
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Reflection of waves can be expressed as the sudden change in the propagation of waves after colliding the interphase of the two distinct mediums.
The phenomenon that bounces anything back can be termed reflection. An example to demonstrate reflection can be a ball that can be thrown against a wall. It can also be observed in the context of energy and momentum conservation. Two cases can be formed in the example of a ball.
One can be if there is an elastic collision between the ball and the wall, due to the return of momentum and incident ray, the ball will bounce back with the same speed. If the case is of an inelastic collision, the speed of the ball bouncing back would be different from any one of the objects, either the ball or wall will absorb both the incident energy and momentum.
Reflection of Waves
However, it is seen that there are parts of an incident ray when it is incident on a surface: one which gets reflected, and the other that is transferred to the other medium. This wave which is transferred can be known as a refracted ray.
If the incident wave is inclined on the boundary, it can be termed as the reflected ray. Snell’s law is obeyed in the case of an incident and refracted ray and the law of reflection is obeyed in case of an incident and reflected ray. For this to occur, there are two forms of surfaces, a fixed end, and a free end.
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| Concept Related Links | ||
|---|---|---|
| Unit of Wavelength | Beats | Doppler effect |
| Longitudinal Waves | Speed of Sound Formula | Standing Wave Normal Mode |
What is Fixed End Reflection?
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Let us assume a scenario where a string is attached to the right end of the wall. When there is the propagation of the pulse through the string, the pulse will extend to the right end of the wall and will be reflected.
As soon as the pulse reaches the fixed end of the wall, it will put a force on the wall. The wall will also put an equal and opposite force on the string due to the third law of Newton.
Fixed End Reflection
Now, this force that is exerted by the wall will also reach back to the point that is opposite to the direction of the incident pulse. As a result, zero displacements take place in the fixed end reflection because the string is fixed.
Although, the reflected pulse and incident pulse will cancel each other due to the opposite signs. Hence, there is a phase difference ∏ or a phase reversal that occurs in the case of a travelling wave.
Key Note of Reflection of WavesThere are several types of waves. Some of them include:
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What is Free End Reflection?
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The free end is when we tie a ring with the right end of a string. The ring without any friction goes up and down around a pole. When we create a disturbance that goes till the right end of the rope, the ring will move upwards and will pull the string by stretching it and will generate a reflected pulse. This will be of the same amplitude and sign as that of the incident pulse.
Free End Reflection
Therefore, in free end reflection, there is a maximum displacement that occurs at the end of the string. This displacement possessed by the ring is twice the amplitude formed by any one of the pulses. This results in the reflection without any phase difference.
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Mathematical Equation for Reflection at a Rigid Boundary
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For a rigid boundary, the incident ray can be termed as:
⇒ yi(x, t) = a sin (kx – ωt)
and the reflected ray can be represented as:
⇒ yr (x, t) = a sin (kx + ωt + π). = – a sin (kx + ωt)
According to the principle of superimposition:
⇒ y = y + y = 0
The reflection of waves in a rigid body will occur with a phase difference of ∏ or 180 degrees.
At an open boundary, the reflected ray will be:
| yr (x, t) = a sin (kx + ωt) |
Reflection at an Open Boundary
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The reflection at an open boundary takes place without the change of phase. In the open boundary, the pulse is generated at the boundary as a result of which the amplitude is maximum at the boundary. This states that the two waves reflected and the incident is in phase with one another which signifies that the phase difference is: \(\varphi\) = 0.
Hence yi (x,t) = a sin (kx – \(\omega\)t)
⇒ yr(x,t) = a sin (kx - \(\omega\)t).
By the use of superposition principle we get:
| yi + yr = 2a sin (kx - \(\omega\)t) |
Previous Year Questions
- Which of the following electromagnetic radiations have the longest wavelength … [NEET 1989]
- 4.0 g of a gas occupies 22.4 litres at NTP … [NEET 2015]
- A standing wave having 3 nodes and 2 antinodes … [NEET 1998]
- For a plane electromagnetic wave propagating in x-direction … [NEET 2021]
- For sky wave propagation of 10 MHz signal … [JCECE 2007]
- A vehicle, with a horn of frequency n is moving with a velocity … [NEET 1998]
- With the propogation of a longitudinal wave through a material medium … [NEET 1992]
- The frequency of sinusoidal wave y … [NEET 1992]
- For production of beats the two sources must have … [NEET 1992]
- The magnetic field in a travelling electromagnetic wave has a peak value … [VITEEE 2018]
- A hollow cylinder with both sides open generates a frequency f in air … [WBJEE 2008]
- If the amplitude of sound is doubled and the frequency reduced to one fourth … [NEET 1989]
- A wave in a string has an amplitude of … [NEET 2009]
- A wave of frequency 100 Hz travels along a string towards its fixed end … [NEET 1994]
- A wave travelling in positive X-direction with … [NEET 2002]
- A wave travelling in the … [NEET 2013]
- A whistle revolves in a circle with angular speed … [NEET 2002]
Things to Remember
- Changes in direction of propagation of waves caused by striking of incident rays on the boundary of distinct mediums is known as reflection of waves.
- An example of reflection of waves is the phenomenon of echo where the person gets the sound as a result of the reflection of waves from the far object.
- The two different surfaces where the reflection of waves takes place are the fixed end and the free end surfaces.
- Phase reversal or a phase difference ∏ occurs in the case of a fixed end reflection.
- There is no phase reversal or phase difference in the case of a free-end reflection.
- For a rigid boundary, the equation of incident ray is yi(x, t) = a sin (kx – ωt) and the equation of reflected ray is yr (x, t) = a sin (kx + ωt + π). = – a sin (kx + ωt).
Sample Questions
Ques: What could be the examples of reflecting waves? (2 Marks)
Ans: Some examples of reflecting waves can be light waves that can be reflected. In the case of sound waves, the phenomenon of echo can be an example that depicts the reflection of waves. The waves in case of an echo get reflected by a distant object and come back to the person after some time.
Ques: Explain the process of reflection of waves that takes place on a string on both its free and fixed end. (2 Marks)
Ans: We get a reflected wave that is inverted from the incident ray in the case of a fixed end on a string. While we get a reflected wave that is not inverted from the incident ray in the case of a free end on a string.
Ques: Explain the standing waves. (2 Marks)
Ans: Standing waves are also known as stationary waves. They can either be a form of transverse wave or longitudinal wave. These types of waves do not cause any forward motion in their neighbouring particles in the form of disturbance beyond a particular region.
Ques: Explain the types of waves. (2 Marks)
Ans: The waves can be of two types namely longitudinal waves and the transverse wave. The longitudinal waves have alternating crests and troughs or compressions and rarefactions like that of sound waves. Transverse waves have this motion in a perpendicular form to the point. Their disturbance is when the surface goes up and down alternately.
Ques: Explain the reflection of waves. (1 Mark)
Ans: When the incident ray hits the border between the various mediums, the direction of the wave’s propagation depicts a change. This phenomenon is known as the reflection of waves.
Ques: Give the mathematical equations of the incident and reflected rays in case of rigid boundaries. (2 Marks)
Ans: The mathematical equations of incident and reflected rays in case of rigid boundaries are gives as:
- Incident Ray: yi(x, t) = a sin (kx – ωt)
- Reflected Ray: yr (x, t) = a sin (kx + ωt + π). = – a sin (kx + ωt)
Ques: Write the phase difference in case of both fixed and free end reflection. (2 Marks)
Ans: For fixed end reflection, the phase difference ∏ occurs or we can say there is a phase reversal that occurs. For a free end reflection, there is no phase difference, and no phase reversal takes place.
Ques: What are some properties of Reflection of Waves? (3 marks)
Ans: Some important properties of the Reflection of waves are:
- The angle of reflection to the normal remains equivalent to the angle of incidence of the normal.
- The incident ray, the reflected ray, and the normal lay in the same plane during the point of incidence.
- The phase of the reflected wave does not change even when the pulse rope is struck on a lesser dense medium.
Ques: When does a Phase reversal occur? (1 Mark)
Ans. Phase reversal or a phase difference ∏ occurs in the case of a Fixed End Reflection.
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