NCERT Solutions Class 11 Physics Chapter 14 Waves

The Class 11 Physics NCERT Solutions Chapter 14 Waves will help students prepare for Boards, JEE Main, JEE Advanced, NEET, CUET and NDA in 2026-27. Every back-exercise question is solved with full working, so students can check each wave-speed calculation, standing-wave mode, beat-frequency count, and Doppler shift step by step.

This is the last chapter of the NCERT textbook, and it ties together oscillations, sound, and the wave picture used across physics.

• CBSE Weightage: 6 to 8 marks, usually one derivation plus one numerical on wave speed, beats or the Doppler effect.
• Questions solved: all Exercise 14.1 onward, covering wave equation, speed on a string, standing waves, beats and Doppler shift.
• Key formulas: progressive wave equation, speed on a string, Newton-Laplace speed of sound, beat frequency, Doppler formula.

Each solution in this Class 11 Physics NCERT Solutions Chapter 14 Waves compilation is curated by subject experts, based on the 2026-27 NCERT textbook, and refined against the last five years of CBSE Board, JEE Main and NEET papers.

Transverse and Longitudinal Waves in Chapter 14 Waves

A wave carries energy and information from one place to another without moving the medium along with it. The chapter opens by splitting mechanical waves into two types. Getting this split right is the first step in almost every numerical, because the wave type decides which medium can carry it.

In a transverse wave, such as a wave on a string, the medium forms crests and troughs. In a longitudinal wave, such as a sound wave in air, the medium forms compressions and rarefactions. Sound cannot travel as a transverse wave through a gas because a gas has no shear strength. The NCERT solutions state this reason in full, so students can justify their answer in the board exam and not just name the wave type.

The Progressive Wave Equation and Its Terms

A travelling wave is written as a single equation that gives the displacement of any particle at any time. The chapter builds every numerical on this one relation, so reading each term correctly is what earns the marks.

The displacement of a wave moving along the positive x-direction is y(x, t) = a sin(kx − ωt + φ). Each symbol has a fixed meaning, and the solved answers pull them out one by one.

• Amplitude (a): the largest displacement of a particle from its rest position.
• Angular wave number (k): equals 2π/λ, where λ is the wavelength.
• Angular frequency (ω): equals 2πf, where f is the frequency.
• Phase (kx − ωt + φ): fixes the state of the particle at a given place and time.

Numericals like Exercise 14.8 and Exercise 14.9 give a wave equation and ask for the amplitude, wavelength, frequency and speed. Read the number multiplying x as k and the number multiplying t as ω, then use v = ω/k. The Class 11 Physics NCERT Solutions Chapter 14 Waves show this extraction on a separate line for every such question.

Speed of a Wave on a String and in Gases

The speed of a wave depends only on the medium, not on the source. The chapter gives one formula for a stretched string and a separate line of reasoning for sound in a gas. Both appear often in the exam, so the solutions derive each one fully.

On a stretched string the speed is v = √(T/μ), where T is the tension and μ is the mass per unit length. A tighter or lighter string carries the wave faster. Questions such as Exercise 14.6 use this relation directly.

For sound in a gas the chapter tells a two-step story that students must know for a full-mark answer.

• Newton's formula: Newton assumed the compressions and rarefactions happen at constant temperature, giving v = √(P/ρ). This value came out about 15% too low for air.
• Laplace correction: Laplace showed the changes are too fast for heat to escape, so they are adiabatic, giving v = √(γP/ρ). This matches the measured speed of sound.

The Laplace correction adds the factor √γ, where γ is the ratio of specific heats. The NCERT solutions explain why the process is adiabatic, not just which formula to use, because CBSE asks for that reasoning in the derivation.

The Principle of Superposition and Reflection of Waves

When two waves meet, their effects add. The chapter states this as the principle of superposition, and it is the idea behind beats, standing waves and interference. The solved answers use it every time two waves share the same medium.

By superposition, the resultant displacement at a point is the sum of the displacements each wave would produce there on its own. Two features follow from this and appear in short-answer questions.

• Constructive addition: when two crests meet, the displacements add and the amplitude grows.
• Destructive addition: when a crest meets a trough, the displacements cancel and the amplitude drops.
• Reflection at a fixed end: the wave flips over, so a crest returns as a trough, a phase change of π.
• Reflection at a free end: the wave returns without flipping, so there is no phase change.

Reflection is what sends a wave back along the string to meet the incoming wave. A fixed end gives a phase reversal of π; a free end gives none. The NCERT solutions for Class 11 Physics Chapter 14 Waves state the boundary rule clearly, because the next topic, standing waves, depends on it.

Standing Waves and Normal Modes on Strings and in Pipes

When a wave and its reflection overlap, they form a standing wave that does not travel. Some points, called nodes, never move; others, called antinodes, swing the most. The allowed patterns are the normal modes, and they set the frequencies an instrument can produce.

The lowest frequency is the fundamental, and the higher ones are overtones. Numericals like Exercise 14.11 ask for the fundamental frequency of a string or a pipe. A pipe closed at one end produces only odd harmonics, so its notes differ from an open pipe of the same length. The solved answers draw the node-antinode pattern in words so students can rebuild it in the exam.

Beats: Frequency, Formation and Uses in Chapter 14 Waves

When two sounds of nearly equal frequency play together, the loudness rises and falls in a slow throb. This throb is called a beat, and it is a direct result of superposition. The chapter gives one simple formula, and the NCERT solutions apply it to every beat question.

The beat frequency equals the difference between the two source frequencies, f_beat = |f₁ − f₂|. Beats form only when the two frequencies are close, usually within a few hertz. The idea appears in these standard exam settings.

• Tuning instruments: a musician tunes a string until the beats with a reference note vanish.
• Finding an unknown frequency: load or file a tuning fork and watch whether the beat rate rises or falls.
• Everyday sound: two engines running at close speeds produce an audible throb.

Questions such as Exercise 14.12 give a tuning fork that produces a known number of beats and ask for the second frequency. The beat count per second is exactly the frequency difference in hertz. The trick is deciding whether to add or subtract, and the solutions show how the change in beat rate settles the sign.

The Doppler Effect for Sound and Its Formula

When a source or a listener moves, the pitch heard is not the pitch sent out. This shift is the Doppler effect, and it is the most-tested single idea in the chapter. The solved answers keep the sign convention fixed so students never lose marks on direction.

The observed frequency is f′ = f (v ± v_o)/(v ∓ v_s), where v is the speed of sound, v_o the observer's speed and v_s the source's speed. The rule for the signs is what students must lock in.

• Approaching: when source and observer move closer, the pitch rises above the emitted frequency.
• Receding: when they move apart, the pitch falls below the emitted frequency.
• Sign rule: choose the signs so that approach always gives a higher f′ and recession a lower one.

Numericals like Exercise 14.19 and Exercise 14.20 ask for the frequency heard when a train or a car passes. Fix the direction of motion first, then pick the signs to match a rise or fall in pitch. The Class 11 Physics NCERT Solutions Chapter 14 Waves put the sign choice on its own line so the reasoning is never hidden inside the arithmetic.

Exercise-wise Breakdown for Class 11 Physics Chapter 14 Waves

The NCERT back-exercise splits into clear groups. Use this map to plan which answers to practise first for the 2026-27 boards. Every group links to the full solved set.

Solving the groups in this order builds the skills in the same sequence the chapter teaches them. Start with wave speed, then the wave equation, then standing waves and Doppler, because each group uses the one before it.

Common Mistakes Students Make in the Waves Chapter

These slips happen while writing or calculating the answer, not because the concept is unclear. Each one costs 1 to 3 marks in the CBSE paper, so the solved answers point them out at the exact step.

Student Feedback on the Waves Chapter

Practice Questions for Class 11 Physics Chapter 14 Waves

Once the solved answers are clear, test yourself on the full question set. The practice page has every NCERT question with a step-by-step Solution and an Expert Solution behind a click.

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