NCERT Notes Class 11 Physics Chapter 14 Waves

These Class 11 Physics Notes Chapter 14 Waves gather every wave type, speed formula, superposition rule, beat and Doppler result that the Boards, JEE Main, JEE Advanced, NEET, CUET and NDA papers actually test in 2026-27. Use them to revise the whole chapter fast, with formulas, definitions and diagrams in one place.

This is the last mechanics chapter of Class 11, and it ties together oscillations, sound and the wave ideas you meet again in optics next year.

• CBSE Weightage: 6 to 8 marks, usually one short answer plus one numerical on wave speed, beats or Doppler effect.
• Topics covered: transverse and longitudinal waves, progressive wave equation, wave speed on a string and in gases, superposition, standing waves, beats and Doppler effect.
• Key formulas: wave speed, Newton-Laplace speed of sound, standing-wave frequencies, beat frequency, and the Doppler shift.

These Class 11 Physics Notes Chapter 14 Waves are curated by subject experts, based on the 2026-27 NCERT textbook, and checked against the last five years of CBSE Board, JEE Main and NEET papers.

Topic-by-Topic Summary of Waves

The chapter builds the idea of a wave step by step. It starts with the two wave types, moves to the equation of a moving wave, then to speed, and finishes with what happens when two waves meet. Here is the quick map of what each topic gives you.

• Wave types: the difference between transverse and longitudinal waves, and where each one is found.
• Progressive wave: the equation of a travelling wave and the meaning of amplitude, wavelength, frequency and phase.
• Wave speed: speed on a stretched string, and the speed of sound in a gas using the Newton formula with the Laplace correction.
• Superposition: the principle of superposition, reflection of waves, and the formation of standing waves and normal modes.
• Beats and Doppler: the beat frequency from two close frequencies, and the Doppler shift when a source or listener moves.

Revise the topics in this order, because each one uses the one before it. Get the wave equation clear first, and the speed and superposition numericals become far easier. These Class 11 Physics Notes Chapter 14 Waves follow the same sequence as the NCERT textbook.

Transverse and Longitudinal Waves in Waves

A wave carries energy and momentum from one place to another without moving the medium as a whole. The chapter splits mechanical waves into two types, based on how the particles move compared with the wave. Getting this split right is the first step in any concept question.

Sound in air is always longitudinal, because a gas cannot support the shear needed for a transverse wave. Transverse mechanical waves travel through solids and along a liquid surface, but not through the body of a gas. Keep this rule ready, since it is a common one-mark objective question in NEET and CUET.

Progressive Wave Equation and Its Terms

A progressive wave moves steadily through a medium and carries energy forward. Its displacement is written as y(x, t) = A sin(kx − ωt). Each symbol in this equation stands for one measurable feature of the wave.

• Amplitude (A): the largest displacement of a particle from its rest position.
• Wavelength (λ): the length of one full wave, linked to the angular wave number by k = 2π/λ.
• Angular frequency (ω): linked to the time period by ω = 2π/T = 2πf.
• Phase: the term (kx − ωt), which fixes the state of a particle at a given place and time.

The wave speed is the ratio of angular frequency to wave number, v = ω/k = λf. A plus sign in the phase means the wave moves in the negative x direction, and a minus sign means it moves in the positive x direction. Read the sign carefully, because it decides the direction in every travelling-wave problem.

Speed of a Wave on a String and in Gases

The speed of a wave depends only on the medium, not on how the wave is made. The chapter gives one formula for a stretched string and one for a gas, and the gas result needs a famous correction. These two speed formulas carry most of the numerical marks in the chapter.

• On a string: the speed is v = √(T/μ), where T is the tension and μ is the mass per unit length.
• Newton's formula for a gas: Newton took sound as an isothermal process and got v = √(P/ρ), which is about 15% too low.
• Laplace correction: Laplace treated sound as an adiabatic process, giving v = √(γP/ρ), which matches the measured value.

Sound travels through a gas by fast compressions and rarefactions, so the process is adiabatic, not isothermal. This is why the Laplace correction multiplies Newton's result by √γ, where γ is the ratio of the two specific heats. The corrected speed for air near room temperature comes out close to 340 metre per second, and this derivation is a favourite three-mark Board question.

Superposition, Reflection and Standing Waves

When two or more waves cross the same point, their displacements add. This principle of superposition is the base for interference, standing waves and beats. The chapter uses it in three linked settings.

• Superposition: the resultant displacement is the sum of the separate displacements at every instant.
• Reflection: a wave hitting a fixed end flips over (a phase change of π), while a wave at a free end reflects without a flip.
• Standing waves: a wave and its reflection add to give fixed nodes (no motion) and antinodes (largest motion), so the pattern does not travel.

A standing wave on a fixed string only survives at certain frequencies called normal modes or harmonics. For a string of length L fixed at both ends, these frequencies are f_n = nv/2L. The lowest frequency is the fundamental, and the rest are its integer multiples. An air column open at both ends behaves the same way, while a pipe closed at one end gives only odd harmonics.

Beats and the Doppler Effect in Waves

The last two topics both come from waves of slightly different frequency or from motion of the source. Beats and the Doppler effect are short but reliable scorers, and both appear as one-line numericals in every exam.

• Beats: two waves of nearly equal frequency give a slow rise and fall in loudness. The beat frequency equals the difference of the two frequencies, f_beat = |f₁ − f₂|.
• Doppler effect: the pitch heard changes when the source or the listener moves. It rises as they approach and falls as they move apart.

The general Doppler formula for sound is f' = f (v ± v_o)/(v −+ v_s), where v_o is the listener speed and v_s is the source speed. Pick the signs so that approach raises the frequency and recession lowers it. Unlike light, the Doppler shift for sound depends on whether it is the source or the listener that moves, because sound needs a medium.

All Formulas for Waves

Every formula you need for the chapter sits in one table below, with its meaning and its SI unit. Learn the wave-speed and standing-wave rows first, since those carry the most marks in both Boards and entrance papers.

Carry the SI unit on every line of your working. Losing the unit is a silent way to drop the final mark even when the number is right. Keep this table open while you solve the back-exercise numericals in these Class 11 Physics Notes Chapter 14 Waves.

Key Definitions and Derivations for Waves

Boards short-answer questions often ask for a clean definition in one or two lines. Learn these word-for-word, because a vague definition loses easy marks. Each one also sets up a derivation you can be asked to show.

A common derivation asks you to prove the standing-wave frequencies of a string fixed at both ends. Fit a whole number of half wavelengths into the length L and use v = fλ to get f_n = nv/2L. The Laplace correction to the speed of sound is the other derivation examiners ask most often.

Common Mistakes Students Make in Waves

These slips happen while writing or calculating, not because the concept is unclear. Each one costs 1 to 3 marks in the paper, so watch for them at the exact step.

Waves Weightage in CBSE Boards, JEE and NEET

This chapter is a steady scorer. It almost always brings a short answer plus one or two numericals, and the topics repeat year after year. Here is how the marks split across the main exams for 2026-27.

Standing waves and the Doppler effect are the two most tested ideas from this chapter across all four exams. Master those first, then beats, then the speed of sound, in that order of return on effort.

How to Revise Waves Quickly

Use these Class 11 Physics Notes Chapter 14 Waves for a fast, ordered recap the night before a test. The checklist below takes about 30 minutes and hits every marks-heavy idea.

• First 10 minutes: write the wave equation, the two wave-speed formulas, and the standing-wave frequency from memory.
• Next 10 minutes: redo one numerical each on wave speed on a string, beat frequency, and a Doppler shift.
• Last 10 minutes: revise the harmonics of open and closed pipes, and the Laplace correction derivation.

Close the loop by sketching a standing wave with its nodes and antinodes. If you can do all three blocks without notes, the chapter is exam-ready. Keep the All Formulas table beside you for the first pass only, then try it closed-book.

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