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Cheat sheet · JEE Preparation Physics

Waves cheat sheet

The whole chapter on one page: key formulas, facts and the points to remember, for quick revision before a test.

JEE · Physics

Cheat sheet

Class 11 · Chapter 14Waves

v = νλ — speed equals frequency times wavelength.

1. Wave Basics

y=asin⁡(kx−ωt+ϕ)y = a\sin(kx - \omega t + \phi)
k=2πλk = \dfrac{2\pi}{\lambda}v=ωk=νλv = \dfrac{\omega}{k} = \nu\lambda
  • Transverse: particles ⊥ to wave direction (string).
  • Longitudinal: particles ∥ to wave (sound in air).

2. Wave Speed

v=Tμv = \sqrt{\dfrac{T}{\mu}} (string)
v=γPρv = \sqrt{\dfrac{\gamma P}{\rho}} (Laplace, gas)

Sound speed in air ≈ 343 m/s at 20 °C; increases with temperature.

3. Standing Waves & Harmonics

SystemFrequencies
String (both ends fixed)νn=nv2L\nu_n = \dfrac{nv}{2L}, n = 1, 2, 3…
Closed pipeνn=(2n−1)v4L\nu_n = \dfrac{(2n - 1)v}{4L} — odd harmonics
Open pipeνn=nv2L\nu_n = \dfrac{nv}{2L} — all harmonics

Nodes are λ/2 apart; antinode to node = λ/4.

4. Beats

νbeat=∣ν1−ν2∣\nu_{beat} = |\nu_1 - \nu_2|

5. Key Points

  • Reflection at a rigid end: phase change of π.
  • Sound needs a medium.
  • Superposition: displacements add.
  • Fundamental = first harmonic.

Remember: v = νλ | √(T/μ) | pipe & string harmonics | beats

Waves: questions and notes

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