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Waves
Physics · Class 11NCERT pp. 278–2952 sets × 25 questions
Key facts and formulas for Waves, three worked sample questions, and two full practice sets. Every question has a hint, a reason for every option and a step-by-step solution, with a calculator or animation where one helps. English and Hinglish.
Formula sheet for this chapter
| Idea | Rule or fact |
|---|
| Wave speed and wavelength | v = νλ = ω/k; k = 2π/λ; y = a sin(kx − ωt) moves towards +x, kx + ωt towards −x |
| Phase difference | Δφ = 2π Δx / λ; same phase means Δx = nλ |
| Speed on a string | v = √(T/μ), μ = mass per unit length |
| Speed in fluids and gases | v = √(B/ρ); Laplace: v = √(γP/ρ), adiabatic; v ∝ √T and v ∝ 1/√M |
| Superposition | Displacements add algebraically; equal waves: A = 2a cos(φ/2) |
| Reflection | Rigid end: phase change π. Free end: no change. Adjacent nodes are λ/2 apart |
| String fixed at both ends | ν = n v / 2L, n = 1, 2, 3 ... (all harmonics) |
| Open pipe and closed pipe | Open: ν = n v / 2L. Closed: ν = (2n − 1) v / 4L, odd harmonics only |
| Beats and Doppler effect | Beats = |ν₁ − ν₂|; ν′ = ν (v ± v_o) / (v ∓ v_s), approach raises pitch |
| Sound level and echo | β = 10 log₁₀(I/I₀); echo: 2d = vt, minimum gap 0.1 s |
Three sample questions
Q1. A progressive wave in a medium transports
- matter, but no energy
- both matter and energy in bulk
- energy and information, but no bulk matter
- neither energy nor information
Hint and solution
Hint: Think of a stadium wave: people stay in their seats, yet something travels around the stadium.
- Wave = moving pattern of disturbance — A wave is a disturbance that moves through a medium. The medium itself does not move forward.
- Particles: oscillate about mean position — Each particle only vibrates near its own place and passes the disturbance to its neighbour.
- Energy + information travel, matter does not — So energy and information are transported, but no bulk matter is carried. Option C.
Answer: C. A wave is a moving pattern. The particles only shuffle about their places, while energy and information travel.
Q2. Which of the following waves can travel through vacuum?
- Radio waves
- Sound waves
- Waves on a stretched string
- Seismic waves
Hint and solution
Hint: Mechanical waves need particles to pass the disturbance on. Which wave here is not mechanical?
- Mechanical wave needs a medium — Sound, string and seismic waves pass through matter by elastic forces between particles.
- Electromagnetic wave needs no medium — Radio waves are made of changing electric and magnetic fields that sustain each other.
- Only radio waves cross vacuum — So the wave that can travel through vacuum is the radio wave. Option A.
Answer: A. Radio waves are electromagnetic. The others are mechanical and need a medium.
Q3. Sound waves in air are
- transverse, made of crests and troughs
- transverse, made of nodes
- electromagnetic
- longitudinal, made of compressions and rarefactions
Hint and solution
Hint: Air resists being compressed but does not resist sliding layers. Which wave type needs only compression?
- Gas: no shear rigidity — A gas cannot hold a sideways shear, so a transverse wave cannot form in it.
- Gas resists compression — Air does resist being squeezed, so a push-pull wave can travel along the direction of motion.
- Sound in air = longitudinal — Such a wave has compressions and rarefactions. Option D.
Answer: D. Air cannot sustain shear, so sound in air is longitudinal.
How to use this chapter
Read the NCERT pages first, then attempt Set 1 without the hints. Note every wrong answer in a mistake list, read the reason for each option, and retry Set 2 two days later. A topic is solid when you can say why each wrong option is wrong.