# Waves Notes, Class 11 Physics | SwaVid

Waves: NCERT Class 11 Physics notes with key ideas, formulas, common mistakes and 3 quick checks with worked answers. Written by SwaVid from the textbook.

Canonical: https://www.swavid.com/cbse/class-11/physics/chapter/waves

Source: https://www.swavid.com/cbse/class-11/physics/chapter/waves

# Waves

## Formulas and definitions

## Key ideas

## Common mistakes

## Quick checks

## Keep going

## Questions parents ask

## Class 11 Physics on SwaVid

### Transverse and longitudinal waves

### Displacement relation for progressive waves

### Speed of mechanical waves

### Principle of superposition

### Standing waves in bounded media

### Beats

### Related chapter

### Related chapter

### Related chapter

### All chapters

SwaVid › CBSE › Class 11 › Physics › Waves

Notes written by SwaVid from the NCERT textbook.

Class 11 Physics, Chapter 14. Key ideas, formulas and common mistakes.

CBSE prints 10 marks for Unit X together, not for this chapter alone.

Short answer. This chapter explains the propagation of mechanical waves, including transverse and longitudinal types, along with their mathematical description. It develops the concepts of wave speed, the principle of superposition, standing waves in strings and pipes, and beats.

Source: NCERT Physics Part II (Reprint 2026-27) , Chapter 14, Waves

In transverse waves, constituents of the medium oscillate perpendicular to the direction of wave propagation, as seen in stretched strings. In longitudinal waves, constituents oscillate along the direction of wave travel, creating alternating compressions and rarefactions, as seen in sound waves.

A harmonic wave travelling along the positive x-direction is represented as y(x, t) = a sin(k x - ω t + φ). Here a is the amplitude, k = 2π / λ is the angular wave number, and ω = 2π ν is the angular frequency.

The speed of a transverse wave on a stretched string depends on tension and linear mass density through v = √(T / μ). For longitudinal sound waves in a fluid, speed is given by Newton's formula corrected by Laplace as v = √(γ P / ρ), where γ is the adiabatic ratio.

When two or more waves overlap, the resultant displacement of any element of the medium is the algebraic sum of the displacements due to each wave. This principle explains interference, standing waves, and beats.

Superposition of two identical waves travelling in opposite directions produces a standing wave, which has stationary nodes with zero amplitude and antinodes with maximum amplitude. Stretched strings and open pipes support all harmonics, whereas a pipe closed at one end supports only odd harmonics.

When two sound waves of slightly different frequencies ν₁ and ν₂ travel in the same direction and superpose, they produce periodic fluctuations in sound intensity. The beat frequency is given by ν beat = |ν₁ - ν₂|.

Try each question first. Then tap it to see the answer.

Linear mass density μ = M / L = (2.0 × 10⁻³ kg) / (0.5 m) = 4.0 × 10⁻³ kg m⁻¹

Wave speed v = √(T / μ) = √(80 / (4.0 × 10⁻³)) = √20000 ≈ 141.4 m s⁻¹

141.4 m s⁻¹

For an open pipe, the fundamental frequency is ν₁ = v / (2 L)

ν₁ = 340 / (2 × 0.85) = 340 / 1.7 = 200 Hz

200 Hz

Beat frequency is given by ν beat = |ν₁ - ν₂| = 4 Hz

ν₂ = 256 + 4 = 260 Hz, or ν₂ = 256 - 4 = 252 Hz

252 Hz or 260 Hz

Oscillations .

Mechanical Properties of Fluids .

Kinetic Theory .

The 14 chapters of Class 11 Physics .

CBSE does not give marks to one chapter. It prints 10 marks for Unit X together (Oscillations and Waves). Waves is part of that group.

No. They are written by SwaVid from the NCERT textbook. The CBSE curriculum is the reference for what is assessed.

This is the last chapter in the NCERT books for Class 11 Physics.

SwaVid is an AI tutor for Indian students in Classes 6 to 12. It finds the earlier ideas a child missed, then teaches today’s chapter. Start free to see how it works.

- Ch 14 NCERT book
- 10 marks, Unit X together
- 3 quick checks
- Confusing wave speed with particle speed . Wave speed is constant for a given medium and equals v = ν λ. Particle speed is the speed of oscillation, given by the time derivative dy/dt, which changes sinusoidally with time and position.
- Using Newton's isothermal formula instead of Laplace's formula for sound in air . Sound propagation in a gas is an adiabatic process, not isothermal. Always include the adiabatic index γ in the expression v = √(γ P / ρ).
- Listing even harmonics for a pipe closed at one end . A pipe closed at one end has a node at the closed end and an antinode at the open end, which permits only odd harmonics (1st, 3rd, 5th, etc.) with frequencies (2n - 1) v / (4 L).
- Misidentifying the direction of wave travel from the phase sign . In y = a sin(k x - ω t), the negative sign between k x and ω t means propagation along +x. A positive sign, y = a sin(k x + ω t), means propagation along -x.

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