AimMent
Exam level4 past questions

Wave Motion and Wave Equation

Learn the fundamentals of wave motion, including the wave equation, its parameters, direction, and the distinction between particle and wave velocities.

Why this shows up in the exam

NEET tests your understanding of wave properties and the mathematical description of waves.

How NEET tests this

Numerical · 3 QsDirect recall

Learn the idea

A travelling sinusoidal wave is described by y = A sin(ωt − kx) (or +kx). The angular frequency ω and wave‑number k give the wave speed v = ω/k, while the particle’s maximum speed is A ω. The key insight is that particle and wave speeds are linked but not the same – one comes from the time‑derivative of displacement, the other from the ratio ω/k.

🧠 Memory hook: Think of a marching band: the drum’s beat (ω) tells how fast each drummer moves (A ω), while the whole band’s marching speed is the beat divided by the spacing between drums (ω/k).

Get this one clearly and it pays off every single time it shows up in the paper. 🎯

Formulas & facts to keep ready

  • Wave equation: y = A sin(ωt − kx) or y = A sin(kx − ωt)
  • ω = 2πf and k = 2π/λ (NCERT)
  • Wave speed v = ω/k = λf
  • Maximum particle velocity v_max = A ω (from dy/dt)
  • Sign of (ωt − kx) tells direction: ‘‑kx’ → +x direction

How to approach it

  1. 11. Write the given equation in the standard form y = A sin(ωt − kx) and read off A, ω and k (pay attention to any factor outside the sine).
  2. 22. Compute maximum particle speed: v_max = A ω.
  3. 33. Compute wave speed: v = ω/k.
  4. 44. Form the required ratio or answer the question using these two values.

Worked example — watch it click

The equation of a simple harmonic wave is given by y = 3 sin (π)/(2) (50t-x) where x and y are in metres and t is in seconds. The ratio of maximum particle velocity to the wave velocity is :

  • ✅(3π)/(2)
  • B)3π
  • C)(2π)/(2)
  • D)2π

The concept behind this problem

The example asks for the ratio of the largest speed of a particle in the medium to the speed at which the wave pattern itself travels – it forces you to extract A, ω and k, compute A ω and ω/k, and compare them.

Step by step

  1. 1Wave equation y = 3 sin(π/2)(50t - x) gives amplitude A = 3 m, ω = 25π rad/s, k = π/2 m⁻¹.
  2. 2Maximum particle velocity = Aω = 3 × 25π = 75π m/s.
  3. 3Wave velocity = ω/k = 25π/(π/2) = 50 m/s.
  4. 4Ratio = 75π/25 = 3π.

Watch out

Students often take the ratio as (A ω)/ω = A, forgetting to use the wave speed ω/k in the denominator.

Common slip-ups that cost marks

  • •Missing the factor that multiplies (50t‑x); it changes ω and k.
  • •Confusing ω with 2πf or k with 2π/λ – use the exact coefficients from the equation.
  • •Using ω/k = v but then dividing by ω again – keep numerator and denominator distinct.

🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.

Practise it

These are real questions from past NEET papers that test this exact idea.

Question 1 of 4NEET 2008

The wave described by y = 0.25 sin(10 πx – 2πt), where x and y are in metres and t in seconds, is a wave travelling along the:

Push further

More challenging

4 harder questions built from the past papers above — a step up in difficulty, with distractors designed so you can't get there by elimination. Written and checked by our reviewers, not from a real paper.

Question 1 of 4

A transverse wave is described by the equation y(x,t) = 0.08 sin(5πx - 15πt), where x and y are in meters and t is in seconds. Determine the direction of wave propagation, its frequency, and its wavelength.

More from Oscillations and Waves