Questions
5–6 MCQs per paper
Difficulty
Medium-Hard
Importance
High yield for JEE Main/Advanced and NEET
Overview
Waves describe the transmission of energy and momentum through a medium via periodic disturbances. This topic is fundamental for JEE and NEET as it forms the basis for optics, acoustics, and modern physics, requiring a solid grasp of phase relationships and wave equations.
Wave Motion and Speed
A wave is represented by the function y(x,t) = f(ax ± bt). The velocity of a wave is determined by the properties of the medium, specifically its elasticity and inertia.
- Wave speed v = ω/k
- Phase velocity v = fλ
- Speed in a stretched string v = √(T/μ)
- Speed of sound in gas v = √(γP/ρ)
- Particle velocity vp = -v * (dy/dx)
Practice PSU exams free on the app
HPCL · BHEL · ONGC · IOCL · SAIL · No login needed
Gamified Learning · Practice Play Progress
Superposition and Interference
The principle of superposition states that the resultant displacement is the algebraic sum of individual displacements. This leads to constructive and destructive interference based on path difference.
- Constructive interference: Path difference Δx = nλ
- Destructive interference: Path difference Δx = (2n-1)λ/2
- Resultant amplitude A = √(A1^2 + A2^2 + 2A1A2 cosφ)
- Intensity I proportional to A^2
Standing Waves
Standing waves form when two identical waves travel in opposite directions in a bounded medium. Energy is localized between nodes and antinodes rather than being transported through space.
- Equation: y = 2A sin(kx) cos(ωt)
- Nodes occur at x = nλ/2
- Antinodes occur at x = (2n-1)λ/4
- Fundamental frequency of string (fixed-fixed): f = v/2L
- Fundamental frequency of organ pipe (closed): f = v/4L
Beats and Doppler Effect
Beats arise from the superposition of waves with slightly different frequencies, creating a periodic rise and fall in intensity. The Doppler effect describes the frequency shift perceived due to relative motion.
- Beat frequency fb = |f1 - f2|
- General Doppler formula: f' = f(v ± vo)/(v ± vs)
- Use sign convention: towards increases frequency, away decreases frequency
- Observer moving towards source increases f'
Formula Sheet
y = A sin(ωt ± kx + φ)
v = √(T/μ)
f' = f(v + vo)/(v - vs)
fb = |f1 - f2|
I = I1 + I2 + 2√(I1I2) cosφ
Exam Tip
Always verify the phase difference between two waves before applying intensity formulas; a simple sign error in path difference calculations is the most common reason for lost marks.
Common Mistakes
- Confusing the phase velocity with the particle velocity (vp is the slope of the wave profile multiplied by wave speed).
- Applying the Doppler effect formula without proper sign conventions for the velocity of the source and observer.
- Ignoring boundary conditions (open vs closed ends) when calculating harmonics for organ pipes.
More Revision Notes
Ready to test yourself?
Play topic-wise Waves questions in Aspirant Arcade — gamified MCQ practice.
Download FreeGamified Learning · Practice Play Progress