Class 11 CBSE Physics – Waves
(Prepared as concise study notes for quick revision and exam‑preparation)
1. Introduction to Waves
| Simple Explanation | A wave is a disturbance that transports energy from one point to another without transferring matter. The disturbance oscillates about an equilibrium position. |
|---|
Key Points
| # | Concept | Why it matters |
|---|---|---|
| 1 | Wave – periodic disturbance that carries energy. | Foundation of all wave phenomena. |
| 2 | Medium – material required for mechanical waves. | Sound needs air, water, strings, etc. |
| 3 | Electromagnetic (EM) waves – do not need a medium; they are self‑propagating electric‑magnetic field oscillations. | Light, radio, X‑ray, etc. |
| 4 | Superposition – two or more waves add linearly at every point. | Gives rise to interference, standing waves. |
| 5 | Speed of wave – (v = f \lambda). | Relates measurable quantities (frequency, wavelength). |
2. Types of Waves
| Type | Medium | Polarisation | Example |
|---|---|---|---|
| Mechanical | Requires medium | Can be longitudinal or transverse | Sound (longitudinal), string vibration (transverse) |
| Electromagnetic | No medium | Transverse, can be linearly, circular, or elliptical | Light, radio waves, microwaves |
Mechanical Waves
- Longitudinal – particle displacement parallel to direction of propagation.
Example: Sound in air. - Transverse – particle displacement perpendicular to propagation.
Example: Waves on a string, EM waves.
Electromagnetic Waves
- Self‑sustaining oscillations of electric & magnetic fields.
- Travel at the speed of light (c \approx 3.00 \times 10^{8},\text{m s}^{-1}) in vacuum.
- Spectrum (frequency/λ): radio → microwave → infrared → visible → ultraviolet → X‑ray → gamma.
3. Wave Parameters & Relationships
| Symbol | Quantity | Units | Formula |
|---|---|---|---|
| (v) | Wave speed | m s⁻¹ | (v = f \lambda) |
| (f) | Frequency | Hz | (f = 1/T) |
| (\lambda) | Wavelength | m | ( \lambda = v / f) |
| (T) | Period | s | (T = 1/f) |
| (A) | Amplitude | m | Peak displacement from equilibrium |
Important Notes
- Higher frequency → higher speed in a given medium (unless dispersion).
- Amplitude relates to energy: (E \propto A^{2}).
- In EM waves, (v = c) independent of frequency (no dispersion in vacuum).
4. Wave Phenomena
4.1 Reflection
- When a wave encounters a boundary, part of it reflects back.
- Law of reflection: angle of incidence = angle of reflection.
- Total internal reflection occurs when wave travels from denser to rarer medium and the incidence angle exceeds the critical angle.
4.2 Refraction
- Change in direction and speed when a wave passes into a different medium.
- Snell’s law: (n_{1}\sin\theta_{1}=n_{2}\sin\theta_{2}), where (n=v_{\text{air}}/v_{\text{medium}}).
- Index of refraction (n = c/v).
4.3 Interference
- Constructive: (n) path difference → (+) wave.
- Destructive: (m\frac{\lambda}{2}) path difference → cancel.
- Double‑slit: bright/dark fringes given by (y = \frac{m\lambda L}{d}).
4.4 Diffraction
- Bending of waves around obstacles/through apertures.
- Significant when obstacle/ slit width ≈ wavelength.
4.5 Standing Waves
- Formed by superposition of two waves of equal frequency traveling in opposite directions.
- Nodes (zero amplitude) and antinodes (maximum amplitude).
- For a string of length (L) fixed at both ends:
[ f_{n} = \frac{n v}{2L}\quad (n=1,2,3,\dots) ] where (v = \sqrt{T/\mu}) (tension/linear density).
5. Doppler Effect
- Frequency change due to relative motion of source & observer.
- Observer moving towards source: (f_{\text{obs}} = f_{\text{src}}\frac{v + v_{\text{obs}}}{v}).
- Source moving towards observer: (f_{\text{obs}} = f_{\text{src}}\frac{v}{v - v_{\text{src