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Reflection of Waves

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Waves are the disturbance created in the surroundings which are used to transport energy from point A to point B without transfer of matter. We also see different types of waves in our surroundings, when we throw a stone in the quiet pond we observe a disturbance travelling in the pond water formed by the striking of the stone this disturbance is called the wave.

Waves are found in many forms such as,

  • Sound Waves
  • Light Waves
  • Water Waves
  • Radioactive Waves
  • Ultraviolet Waves
  • Mechanical Waves

Energy is transferred through waves. The reflection of waves is the bouncing back of the wave after striking a hard surface.

In this article, we will learn about the reflection of waves, the laws of reflection of waves, etc.

What is Reflection of Waves

When a wave travelling in any medium hit the boundary it returns back in the medium after striking. This phenomenon is called Reflection of Waves

In the phenomenon of reflection, waves obey the same laws as light waves. The reflection of a wave from a boundary surface depends on the nature of the boundary surface. Depending on the nature of the progressive wave, the reflection at the boundary surface can be of the following two types,

  • Fixed End Reflection
  • Free End Reflection

When a progressive wave travelling through a rarer medium is reflected from a denser medium, it is called Reflection at the hard wall, and when a progressive wave travelling through a denser medium is reflected from a rarer medium, it is called Reflection at the free end.

Laws of Reflection

All the waves in nature follow the laws of reflection. The most general example of this is the laws of reflection of light.

The law of reflection states that,

  • The incident wave, the reflected wave and the normal at the point of interaction of the wave all lie in the same plane.
  • When a wave reflects off a plane surface, the angle of incidence is equal to the angle of reflection. 

We can mathematically represent the law of reflection as,

∠i = ∠r

where,
∠i is the angle of incidence
∠r is the angle of reflection

Common Types of Wave Reflection

Many types of waves reflect and their reflection is used for different purposes such as,

  • SONAR or Bat uses sound waves reflection to navigate and found their path.
  • Human eyes see the world because of the reflection of the light wave
  • To study the interior of the earth and the ocean bed we use the reflection of Sescemic waves.

Fixed End Reflection

Suppose the end B of a string AB is tied to a rigid base, a wave pulse is sent from its end A from left to right. If the displacement of the particles in this pulse is upward. When this pulse reached a firm base, it exerts a force on the base in an upward direction. Consequently, according to Newton’s third low motion, a firm base that exerts the same reaction force produces a pulse that starts moving in the opposite direction (from right to left) with the help of a string. This is reflected pulse. 

Fixed End Reflection

In the incident pulse and the reflected pulse, the particles of the string vibrate in opposite directions. Thus, when a pulse is reflected from a rigid boundary, it gets inverted with respect to the incident pulse.  That is, as a result of reflection from the rigid boundary, there is a change of pi or 180° in the phase of the incident pulse. 

If the equation of the incident wave is,

y = A sin 2π / λ (vt – x)

Then the equation of the reflected wave will be,

y = A sin 2π / λ (vt + x + π)

y = – A sin 2π / λ (vt + x)      (because sin( θ – π ) = -sin θ)                                  …… (1)

Thus, if the equation of the incident wave is, 

y = A sin(ωt – kx)

Then the equation of the reflected wave will be,

y = -A (ωt + kx)               …… (2)

It is assumed that the incident wave is traveling in the positive direction along the X-axis and the reflected wave is traveling in the negative direction along the x-axis. When a progressive wave traveling from a denser medium gets reflected in a rarer medium, it is called Fixed End Reflection.

Free End Reflection

Suppose the end B of the string AB is attached to a small ring which can make frictionless oscillations in a vertical rod. A wave pulse is sent from left to right in the string. Suppose the displacement of the particles of the string is upwards. When this pulse reaches end B, it exerts an upward force on this end B. Hence the ring attached to end B moves upwards. 

While returning, this ring crosses the equilibrium position due to inertia. In this case, the ring exerts a reaction force on the string, due to which the same type of pulse starts moving in the opposite direction in the string. Thus, in the incident pulse and the reflected pulse, the particles of the string vibrate in the same direction. It is clear that there is no change in the phase of the incident pulse as a result of reflection from the free boundary.

Free End Reflection

Thus, if the equation of the incident wave is,

y = A sin 2π / λ (vt – x)

Then the equation of the reflected wave will be,

y = A sin 2π / λ (vt + x)…… (3)                                              (because sin(θ – π) = -sin θ)

Thus, if the equation of the incident wave is, 

y = A sin(ωt – kx)

Then the equation of the reflected wave will be,

y = A (ωt + kx)….. (4)

Reflection of Longitudinal Wave from Rigid End

If end B of spring AB is tied to a rigid base. With the help of this spring, a compression pulse is sent from left to right (from A to B). When the pulse reaches end B, it exerts a force on a rigid base from left to right. According to Newton’s third law of motion, a rigid base exerts an equal reaction force on the spring end B from right to left. 

As a result, the compression pulse starts moving from end B to end A with the help of spring. In the incident pulse and the reflected pulse, the directions of displacement of the spring particles are opposite. Therefore, in the case of reflection from a rigid base, the phase of the incident pulse changes by π or 180°.    

Reflection of Longitudinal Wave from Rigid End and Free End

In this situation also, the reflected wave can be represented by equation (1) or (2).

Reflection of Longitudinal Wave from Free End

Let AB be a spring. A compression pulse moves from end A to B i.e. from left to right with the help of spring. When it reaches the free end B, the pulse exerts a force on B from left to right. Due to this force, end B crosses the equilibrium position and moves to the right. Hence, the length of the spring increases, and the rarefaction pulse starts moving from right to left, but still, the direction of displacement of the spring particles remains the same. Therefore, there is no change in its phase due to the reflection of the longitudinal pulse from the free boundary.

In this situation also, the reflected wave can be represented by equations (3) or (4).

Reflection of Sound

As we know all the waves get reflected when struck with a hard surface. Sound waves are no different they also get reflected striking a barrier.

Reflection of sound waves implies that sound waves after hitting a hard surface get reflected back in the same medium.  The only necessary condition of the sound wave is that the surface through which sound has to get reflected must be bigger than the wavelength of the sound wave.

The concept of reflection of the sound wave is used in musical instruments, megaphones, etc.

Laws of Reflection of Sound

Similar to the Law of reflection of light, sound also follows the law of reflection of sound. The laws of reflection of sound are,

Law 1: The Incident wave, reflected wave and the normal to the reflecting surface at the point of incidence all lie in the same plane.

Law 2: Angle of Incidence of the wave is equal to the Angle of Reflection of the wave.

Learn more about, Reflection of Sound

Application of Reflection of Waves

Reflection of waves is the most widely used concept in science. Some of the  most common applications of the reflection of waves are,

Echo

If we utter some words standing at some distance near a hill, tall building, big tree, etc., then due to reflection, the same words are heard again. This phenomenon is called Echo. Thus, the phenomenon of repetition of sound due to the reflection of sound from a rigid boundary is called echo.

The condition for the human ear to hear an echo is that the reflected sound must reach the ear after 0.1 sec as our brain takes 0.1 sec to process the incoming sound waves. As we know the general speed of sound in air is 330 m/s the general distance at which we can hear an echo is calculated to be 17 m.

Echo

 

Sonar

SONAR Its full name is “Sound Navigation and Ranging”. It is based on the principle of reflection of ultrasonic waves. With its help, the position of anybody inside the sea such as a rock, enemy submarine, etc. is detected.  The depth of the sea is also known by this technique.

Read More,

FAQs on Echo

Q1: What is Reflection of Wave?

Answer:

When a wave strikes a barrier at an angle it is sent back in the opposite direction and continues to propagate in that direction. This phenomenon is called the reflection of the wave.

Q2: What is an Example of Reflection of Wave?

Answer:

There are various examples of the reflection of waves. Some of them are,

  • Reflection of light
  • Echo, etc.

Q3: What is an Echo?

Answer:

When a sound wave gets reflected after striking a hard surface it is called an echo.

Q4: What type of Waves can be Reflected?

Answer:

All the waves are caused by a disturbance in the energy patterns. Any type of wave can be reflected after hitting a barrier. Thus, we conclude that any wave may it be a light wave, sound wave, etc all can be reflected.

Q5: What is a Real-Life Example of Reflection?

Answer:

Some real-life examples of reflections are,

  • The image we see in the mirror is caused by the reflection of the light waves.
  • All the light coming to our eyes which enables us to see the world comes to us through reflection.
  • SONAR technology uses the concept of reflection of waves.


Last Updated : 04 Feb, 2024
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