Water, music, light, and even the vibrations we experience when we touch a surface are all made of waves. Reflection is one of waves’ primary characteristics. In a nutshell, reflection occurs when a wave strikes a boundary or surface and returns to the original medium rather from being absorbed or passed through.
What is Reflection of Waves?
A portion (or all) of the wave energy returns to the original medium when it passes through a barrier or another medium. Reflection is the term for this wave’s bouncing back.
We are sure we have looked in a mirror. That is the reflection of light waves. In a similar layer, we will hear an echo caused by sound waves reflecting if we shout in a large, deserted hall or next to a mountain.
Reflection from a fixed end: A rope is fixed at one end to a wall. A pulses created at the other end travels to the fixed end and after reflection returns inverted. There is phase a phase change of π between the incident and the reflected wave.
yi = A sin(ωt – kx)
yr = A sin (ωt + kx + π)
Pulse propagating along along a string is reflected at the fixed end. The reflected pulse is inverted relative to the original pulse.
Boundary condition y(t) = 0
Reflection from a fixed end can be represented by superposition of two pulses one inverted with respect to other, travelling in opposite directions. At boundary resultant is always zero.
Reflection from a free end: If the reflecting end is free to move transversely, a wave is reflected at the boundary. In this case reflected wave is not inverted compared to incident wave. There is no phase change between the incident and reflected wave.
yi = A sin(ωt – kx)
yr = A sin (ωt + kx)
The displacement at the free end is twice the amplitude of the incident wave. Reflection from free end can be represented by the superposition of two waves travelling in opposite direction.
Standing waves and normal modes: Any stationary waves can be formed by the addition of the of two travelling waves moving in opposite directions having same amplitude, frequency, wavelength and speed.
Standing wave in an organ pipe: Organ pipes are musical instruments which are used for producing musical sound by blowing air into the pipe. It works on the principle of the superposition of incident and reflected longitudinal waves.
How Does Reflection Happen?
Consider tossing a ball in the direction of a wall. After striking the wall, the ball bounces back. Waves exhibit relatively similar behavior. When a wave reaches a boundary:
Some of the wave may be reflected back. Some might be absorbed by the surface, while others might be transferred (into the new medium). We concentrate on the wave that returns in pure reflection.
Types of Reflection
The type of border determines how the reflected wave behaves:
1.Reflection at a fixed end or stiff boundary:
o The wave inverts, returning with a 180° phase difference or a negative sign.
An illustration would be a wave pulse that bounces back upside down on a rope that is securely fastened to a wall.
2. Introspection at a free end or boundary:
There is no phase shift or inversion of the wave.
As an illustration, the wave pulse returns without flipping if the end of a rope is hanging loosely.
When a wave pulse is inverted, it reflects and moves downhill if it was initially flowing upward (and vice versa).
Laws of Reflection
Similar to how light is reflected, waves also follow two significant laws:
The angle of incidence is equal to the angle of reflection.
Angle of incidence (i): The angle formed by the normal, which is a line perpendicular to the surface, and the incident wave.
Angle of reflection (r): The angle formed by the normal and the reflected wave. i = r.
The incident wave, reflected wave, and normal all lie in the same plane.
This implies that a flat piece of paper can represent them.
Regardless of whether we are discussing sound, water, light, or any type of mechanical wave, these laws are everywhere.
Reflection in Different Media
Sometimes, the medium after the boundary may be different. Then, the behaviour can change:
From lighter to heavier medium (like air to water):
Part of the wave is reflected with inversion.
From heavier to lighter medium (like water to air):
The reflected wave is not inverted.
This concept also explains reverberations, echoes, and even the difference in sound between a guitars played in a furnished and an empty room.
Phase Change upon Reflection
As previously stated, a wave experiences a 180° (or π radians) phase change when it reflects off a stiff boundary. This implies that a wave’s peak turns into a trough and vice versa.
However, at a free boundary, there is no phase change.
Difference between travelling and standing waves:.
Sl no. | Travelling waves | Standing waves |
1 | In travelling wave, the disturbance produced in a region propagates with a definite velocity. | In standing wave, it is confined to the region where it is produced. |
2 | In travelling wave, the motion of all the particles are similar in nature. | In a standing wave, different particles move with different amplitudes. |
3 | In a standing wave, the the particles at nodes are always at rest. | In travelling waves, there is no particle which always remains at rest. |
4 | In standing wave, all the particles cross their mean positions simultaneously. | In a travelling wave, there is no instant when all the particles are at the mean positions together. |
5 | In standing wave, all the particles between two successive nodes reach their extreme positions together, thus moving in phase. | In travelling wave, the phases of nearby particles are always different. |
6 | In different wave, energy is transmitted from one region of space to other. | In standing wave, the energy of one region is always confined in that region. |
Applications of Reflection of Waves
Reflection of waves is not just theoretical; it has many uses:
Sonar: Ships use sound reflection to detect objects underwater.
Musical Instruments: The design of instruments like drums and guitars takes wave reflection into account for better sound.
Medical Imaging: Ultrasound machines use reflection of sound waves to create images of the inside of the body.
Architecture: Concert halls are designed so that sound reflects in ways that enhance the listening experience.
End correction:
The wave on reaching the open end is not reflected exactly from the open end. It is reflected from a little above the open end. The distance above the open end where pressure node is formed is called end correction (e).
End correction depends on the radius of the organ pipe and is determined experimentally e = 0.6 r or e = 0.3 d.
Summary
When waves return to a boundary, reflection occurs.
Free limits do not result in inversion; rigid boundaries do.
The incident wave, reflected wave, and normal are all in the same plane according to the law of reflection, which states that angle of incidence equals angle of reflection.
The type of border determines the phase shifts.
Sound, water, and light all show wave reflection, which has significant uses.
The phenomenon known as “wave reflection” occurs when a wave hits a boundary or obstruction and returns to its original medium. Part (or all) of the wave energy returns rather than crossing the border.
The angle of incidence and angle of reflection are equal (i = r), according to the two rules of reflection.
• The normal to the surface, incident wave, and reflected wave are all located in the same plane.
A wave becomes inverted when it bounces off a stiff barrier, such as a fixed wall. This implies that a dip reflects as a crest and a crest reflects as a trough. A 180° (π radian) phase shift occurs.
No, a wave does not invert when it reflects from a free barrier, such as the loose end of a rope. There is no phase shift and the reflected wave is oriented in the same direction as the incident wave.
The reflected wave is inverted when it is reflected from a denser medium, such as air to water.
The reflected wave does not invert when it is reflected from a rarer medium, like as water to air.