Chapter 14 — Waves

Chapter 14 of the Class 11 Physics NCERT textbook, "Waves", explains patterns of disturbance that propagate through a medium without physical transfer of matter—transporting energy and information. Mechanical waves include transverse waves (oscillations perpendicular to propagation) and longitudinal waves (oscillations parallel to propagation), with speeds set by the medium's elastic and inertial properties.

• What waves carry and how they move — Mechanical waves need a material medium and transport energy without moving matter along with them. Transverse and longitudinal types differ in whether the medium oscillates across or along the direction of travel.
• Describing and speeding waves — A sinusoidal wave is captured by amplitude, wavelength, frequency, and speed, and the speed is set by the medium—tension and density for strings, elasticity and density for sound—rather than by the source.
• Superposition, standing waves, and beats — When waves overlap, superposition produces interference, standing waves with fixed nodes and antinodes on bounded strings, and beats from close frequencies. Reflection at boundaries and normal modes explain the specific frequencies instruments produce.

1. 01Mechanical waves propagate disturbances through elastic media without transferring matter; they transport energy and depend on medium properties (tension/density for strings, bulk modulus/density for fluids).
2. 02Transverse waves (oscillation ⊥ to propagation) occur in solids; longitudinal waves (oscillation ∥ to propagation) occur in all elastic media; wave speed is independent of frequency in non-dispersive media.
3. 03Sinusoidal wave equation y(x,t) = a sin(kx − ωt + φ) describes position-time evolution with amplitude a, angular wave number k = 2π/λ, angular frequency ω = 2πν, and initial phase φ.
4. 04Wave speed on a string: v = √(T/μ) where T is tension and μ is linear mass density; for sound in media: v = √(B/ρ) (bulk modulus/density) or v = √(γP/ρ) for ideal gases (Laplace correction).
5. 05Principle of superposition: net displacement = sum of individual wave displacements; produces interference (amplitudes add if in-phase, cancel if π out-of-phase), standing waves on bounded strings, and beats (frequency = |ν₁ − ν₂|).
6. 06Reflection at rigid boundaries causes π phase reversal; standing waves with fixed nodes (zero displacement) and antinodes (maximum displacement) λ/2 apart; normal modes restrict frequencies—strings fixed at both ends vibrate at νₙ = nv/(2L), pipes closed at one end at ν = (n + ½)v/(4L).