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Mechanical Waves formula sheet

Every formula in the Mechanical Waves chapter for JEE Main, with one line on when it applies. Topic 1 is open to everyone; sign in free to read all 19 and download the PDF.

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How we count: 7× asked means 7 past JEE Main questions in the PrepWiser bank needed that formula, and "last" is the latest year one appeared. ★ marks formulas asked 8 or more times.

Wave motion and the wave equation

Travelling wave
6× asked, last 2025
y=Asin⁡(kx−ωt+ϕ),y=f(x−vt)y=A\sin(kx-\omega t+\phi),\qquad y=f(x-vt)
kxkx, ωt\omega t opposite signs: along +x+x; same signs: along −x-x. f(ax±bt)f(ax\pm bt): speed b/ab/a.
Wave parameters
11× asked, last 2026
k=2πλ,ω=2πf=2πT,v=fλ=ωkk=\frac{2\pi}\lambda,\qquad \omega=2\pi f=\frac{2\pi}T,\qquad v=f\lambda=\frac\omega k
Speed set by the medium, frequency by the source. vv = coefficient of tt ÷ coefficient of xx.
Phase difference
3× asked, last 2025
Δϕ=2πλ Δx,Δϕ=2πT Δt\Delta\phi=\frac{2\pi}\lambda\,\Delta x,\qquad \Delta\phi=\frac{2\pi}T\,\Delta t
Points λ\lambda apart move alike; λ/2\lambda/2 apart: opposite velocities.
Particle velocity and acceleration
3× asked, last 2025
vp=∂y∂t=−v∂y∂x,ap=−ω2y,vp,max⁡=Aωv_p=\frac{\partial y}{\partial t}=-v\frac{\partial y}{\partial x},\qquad a_p=-\omega^2y,\qquad v_{p,\max}=A\omega
vp,max⁡/v=2πA/λv_{p,\max}/v=2\pi A/\lambda. Wave to the right: rising slope moves down.

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Practise Mechanical Waves

15 more formulas in 5 topics

Speed of a transverse wave on a string, Energy and intensity, Superposition and interference, Reflection and standing waves and Standing waves on strings and pipes. Read the first part free. Sign in free with Google to read the rest and download the PDF.

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Speed of a transverse wave on a string

  • Wave on a stretched string7×
  • Wire of given density and radius3×
  • Hanging rope1×
  • Load hanging in a liquid

Energy and intensity

  • Power along a string
  • Intensity from a source1×

Superposition and interference

  • Two waves of the same frequency5×
  • Intensity of coherent waves1×
  • Path difference from two sources2×

Reflection and standing waves

  • Reflection
  • Standing wave2×

Standing waves on strings and pipes

  • String fixed at both ends10×
  • Sonometer4×
  • String fixed at one end
  • Organ pipes14×

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About 60 past JEE Main questions from this chapter, with instant answer checking and step-by-step solutions where available. Free, and you can start without signing up.

Practise Mechanical Waves

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Version 1, October 2026. Free to share for study, as it is. Please don't sell it or remove the PrepWiser name.

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