Reflection of Waves in Physics: Echoes, Phase Changes & Normal Modes for Class 11 NCERT

What is Reflection?

We can define reflection as a phenomenon that occurs when a wave returns to its original medium after striking a boundary or barrier. This is governed by specific principles and followed by phase or amplitude changes. Reflection applies to light waves, sound waves, and water waves, among others. 

The idea behind this is that when waves hit a boundary between two different materials, they do not disappear. They can meet three conditions. They bounce back, bend, or get absorbed. This is the first aspect of understanding the meaning of the reflection of waves. 

Reflection vs. Refraction

Also, remember not to get confused with a similar phenomenon taught in optics class 11, known as refraction. Here are some differences between reflection and refraction to quickly refer to, in case, you forget. 

Feature	Reflection	Refraction
Definition	This is when light or sound waves bounce back after hitting a surface.	This refers to the bending of light rays as they move from one medium to another with different optical densities.
Cause	It happens when light hits a surface like a mirror and reflects back into the same medium.	This occurs when light travels between two transparent media (like air to water) and changes its direction.
Surface Involved	This takes place on shiny surfaces such as mirrors and polished metals. For sound, it could be boundaries of canyons or tunnels, or walls of empty rooms.	This happens at the boundary between two media, such as air and glass or air and water.
Direction Change	Here, light remains in the same medium, only changing its direction.	In this case, light enters a new medium, which alters both its speed and direction.
Laws Applicable	It follows the Laws of Reflection, where the angle of incidence equals the angle of reflection.	It adheres to Snell's Law of Refraction, which connects the angle of incidence to the angle of refraction.
Speed of Light	There’s no change in the speed of light.	The speed of light varies depending on the refractive index of the medium.
Real-World Examples	Think of looking in a mirror, the echo of sound, or the reflection on a water surface.	Examples include a pencil in water appearing bent, lenses in glasses, and the formation of rainbows.

 

 

Before we dive into learning which type of boundaries allow waves to bounce, absorb, or bend, let's take a step back to learn the laws of reflection. This would be brief, but hang on. 

• Angle Law: The angle of incidence equals the angle of reflection (i = r)
• Plane Rule: Incident wave, reflected wave, and the normal all lie in the same plane
• Frequency Conservation: The frequency remains unchanged during reflection (ωᵢ = ωᵣ)

These laws apply whether you're dealing with sound waves, string waves, or any other type of wave motion, as described under transverse and longitudinal waves. 

 

There are three ways travelling waves hit boundaries, as we were looking at before. 

1. The Rigid Wall: When Waves Hit a Brick Wall, It's a Fixed End Reflection 

If you throw a ball against a concrete wall, it bounces back. 
Waves also do something similar, and it's called a fixed-end reflection.

Newton's Third Law in Fixed End Reflection: So when a wave pulse reaches a fixed end, it exerts force on the rigid wall. So, we already know about Newton's Third Law, which will dictate the phenomenon of the wall exerting an equal and opposite force back. 

But, since these mechanical waves are not in the solid medium, there is something else going on. They completely flip their phase. What this means, if the wave was going up when it hit the wall, it comes back down.
To see the maths behind this, consider
For a wave, y = Aᵢsin(ωt - kx) hitting a rigid boundary

Reflected wave: y = -Aᵣsin(ωt + kx)

Now the negative sign shows that it's a 180° phase change.
Why does this happen?
The rigid boundary will not move. Instead, it forces the wave to have zero displacement at that point.

This type of change in the phase that takes 180 degrees defines the principles of echoes. 

It’s like the phase flips when you hear your echoes after a short delay when you shout in a tunnel. The sound wave from you goes and hits a boundary that is a rigid wall out here. That bounces back. 

2. The Open Boundary: When Waves Have Freedom, It's a Free End Reflection

The wave does not always have to hit a rigid wall to reflect.
In reality, you can take the example of throwing a ball to a curtain which is way less rigid than a wall. The ball does not come back but drops down, with little reflection. Also there is no change in the phase. This type of reflection is a free end reflection. 

We show that in physics as y = Arsin(ωt - kx)

Standing waves are those which reflect between two boundaries. This observation is called standing as the waves or their reflections don’t move from place to another. The best example is a guitar string. When you pluck it, the string is tied at both ends. The pattern here is like standing until it vibrates. 

Points of Standing Waves

• Nodes: Standing waves have points that never move and energy is cancelled out.
• Antinodes: Standing waves can also have points where you can observe the most movement. These are where the wave energy concentrates and creates the biggest oscillations.

The distance between consecutive nodes (or antinodes) is always λ/2. This simple relationship becomes your key to solving complex wave problems. 

Normal modes form when waves reflect back and forth, which causes constructive and destructive interference.

Every system has its favourite frequencies. They are the natural modes of vibration. This is why you see

• Guitar strings produce specific musical notes
• Organ pipes create distinct tones
• Buildings have resonant frequencies (important for earthquake engineering!)

System	Fundamental Frequency (ν₁)	Harmonics	Notes
String Fixed at Both Ends	ν = v / 2L	νₙ = n(v / 2L), where n = 1, 2, 3...	All harmonics present
Air Column (One End Closed)	ν = v / 4L	νₙ = n(v / 4L), where n = 1, 3, 5...	Only odd harmonics
Air Column (Both Ends Open)	ν = v / 2L	νₙ = n(v / 2L), where n = 1, 2, 3...	All harmonics present

When tackling wave reflection problems, here are some steps.

1. Identify the boundary type - rigid, open, or interface
2. Apply the laws of reflection - remember i = r and frequency conservation
3. Determine if there's a phase change - crucial for interference calculations
• Rigid/denser medium: 180° phase change (add negative sign)
• Free/rarer medium: no phase change
4. Use the standing wave equation - y(x,t) = 2a sin kx cos ωt
5. Apply boundary conditions - nodes at fixed ends, antinodes at free ends
6. Calculate normal modes - use the appropriate formula for your system
7. For echoes - always use t = 2d/v (don't forget the factor of 2!)

In case, you need to revise Physics chapters in Class 11 before your finals or competitive tests, here are expert-written notes for all. Within these, you will also find topic-wise guides aligned with the latest NCERT curriculum of 2025-26. 

Units and Measurements Class 11 Notes	Mechanical Properties of Solids Class 11 Notes
Motion in a Straight Line Class 11 Notes	Mechanical Properties of Fluids Class 11 Notes
NCERT Class 11 Notes for Motion in a Plane	Thermal Properties of Matter Class 11 Notes
Laws of Motion Class 11 Notes	Thermodynamics Class 11 Notes
Work, Energy, and Power Class 11 Notes	Kinetic Theory of Gas Class 11 Notes
System of Particles and Rotational Motion Class 11 Notes	Oscillations Class 11 Notes
Gravitation Class 11 Notes	Waves Class 11 Notes

Click on these additional links for Class 11 Science revision notes.

NCERT Class 11 Notes for PCM

NCERT Class 11 Physics Notes