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Waves

NCERT Class 11 Physics Chapter 14

Waves for Class 11 Physics, JEE and NEET: transverse, longitudinal and progressive waves, wave speed, superposition, standing waves, organ pipes and beats.

8 topics Updated 8 Nov 2026

For: Class 11, JEE and NEET, unless a topic says otherwise

In the syllabus: JEE Class 11 syllabus, NEET Class 11 syllabus

With your textbook

NCERT Physics Part II (Class 11), Chapter 14 “Waves”, reprint 2026-27.

Open the official NCERT chapter (PDF, 2.0 MB, ncert.nic.in)

Checked on 19 Oct 2026.

Learn in this order

  1. Wave motion

    Mechanical, electromagnetic and matter waves, local oscillation, energy transport and worked examples.

    NCERT Section 14.1 12 min read 5 solved examples 6 practice questions

  2. Transverse and longitudinal waves

    Particle motion, compressions and rarefactions, which media carry which waves, examples.

    NCERT Section 14.2 13 min read 5 solved examples 6 practice questions

  3. Displacement relation for a progressive wave

    y = a sin(kx − ωt + φ), amplitude, phase, wavelength, k, ω and frequency, with solved examples.

    NCERT Section 14.3 15 min read 5 solved examples 6 practice questions

  4. Speed of a travelling wave

    v = λν, waves on a string, speed of sound, Newton’s formula and the Laplace correction, examples.

    NCERT Section 14.4 17 min read 5 solved examples 6 practice questions

  5. Principle of superposition of waves

    Adding displacements, resultant amplitude 2a cos(φ/2), constructive and destructive interference.

    NCERT Section 14.5 11 min read 5 solved examples 6 practice questions

  6. Reflection of waves and standing waves

    Reflection at a rigid or free end, nodes and antinodes, harmonics of strings and open and closed organ pipes.

    NCERT Section 14.6 17 min read 6 solved examples 6 practice questions

  7. Experiment: speed of sound with a resonance tube

    Finding the first two resonance lengths, v = 2ν(l − l), the end correction, precautions and errors.

    JEE and NEET only 13 min read 5 solved examples 7 practice questions

  8. Beats

    Why two close frequencies give a loudness that rises and falls, beat frequency ν − ν, and tuning with beats.

    NCERT Section 14.7 11 min read 5 solved examples 8 practice questions

Key formulas in this chapter

Wave motion

  • c = 299 792 458 m s (all electromagnetic waves, in a vacuum)
  • distance = speed × time (for a wave travelling at constant speed)
  • 1 light year = c × 1 year ≈ 9.46 × 10 m

Transverse and longitudinal waves

  • distance = speed × time (for a wave travelling at constant speed)
  • arrival gap: Δt = d/vS − d/vP (two waves of speeds vP and vS)
  • distance from the gap: d = Δt × vP vS/(vP − vS)

Displacement relation for a progressive wave

  • y(x, t) = a sin(kx − ωt + φ) (wave along +x)
  • y(x, t) = a sin(kx + ωt + φ) (wave along −x)
  • k = 2π/λ
  • ω = 2π/T = 2πν
  • Δφ = 2πΔx/λ (points Δx apart)

Speed of a travelling wave

  • v = λν = ω/k
  • v = √(T/μ) (string)
  • v = √(B/ρ) (fluid); v = √(Y/ρ) (solid bar)
  • v = √(γP/ρ) (ideal gas, Laplace)

Principle of superposition of waves

  • y = y + y (at every x and t)
  • y = 2a cos(φ/2) sin(kx − ωt + φ/2)
  • A = |2a cos(φ/2)|
  • φ = 0: A = 2a (constructive); φ = π: A = 0 (destructive)

Reflection of waves and standing waves

  • y = 2a sin kx cos ωt (standing wave)
  • nodes: x = nλ/2; antinodes: x = (n + ½)λ/2
  • νn = nv/2L (string fixed at both ends; pipe open at both ends)
  • ν = (2n + 1)v/4L, n = 0, 1, 2, … (pipe closed at one end)

Experiment: speed of sound with a resonance tube

  • l + e = λ/4; l + e = 3λ/4
  • v = 2ν(l − l)
  • e = (l − 3l)/2
  • v0 = vt √(273/T) (T in kelvin)

Beats

  • s = [2a cos ωb t] cos ωa t
  • ωb = (ω1 − ω2)/2; ωa = (ω1 + ω2)/2
  • νbeat = |ν1 − ν2|
  • string: ν ∝ √T (tighter string, higher frequency)

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