Summary

• A wave is a disturbance that propagates through a medium without transporting matter; it transfers energy and momentum.
• Mechanical waves require a medium (e.g., sound, water waves); electromagnetic waves do not (e.g., light).
• Transverse waves: particles oscillate perpendicular to wave velocity (e.g., string waves). Longitudinal waves: particles oscillate parallel to wave velocity (e.g., sound in air).
• For a sinusoidal wave travelling along $+x$: $y(x,t) = A \sin(\omega t - kx + \phi)$, where $A$ = amplitude, $\omega = 2\pi f$ = angular frequency, $k = 2\pi/\lambda$ = wave number, $\phi$ = initial phase.
• Wave speed on a string: $v = \sqrt{T/\mu}$, where $T$ = tension, $\mu$ = mass per unit length.
• Speed of a longitudinal wave in a fluid: $v = \sqrt{B/\rho}$, where $B$ = bulk modulus, $\rho$ = density. In a solid rod: $v = \sqrt{Y/\rho}$, where $Y$ = Young's modulus.
• Principle of superposition: net displacement = sum of individual displacements. Leads to interference, beats, and standing waves.
• Interference: constructive when path difference $= n\lambda$; destructive when path difference $= (n+1/2)\lambda$.
• Beats: periodic variation in intensity when two waves of slightly different frequencies superpose. Beat frequency $f_b = |f_1 - f_2|$.
• Standing waves: formed by superposition of two identical waves travelling in opposite directions. Nodes (zero displacement) and antinodes (maximum displacement) are fixed.
• For a string fixed at both ends, allowed frequencies (harmonics): $f_n = n\frac{v}{2L}$, $n = 1,2,3,\dots$. Fundamental ($n=1$) is the first harmonic.
• For an open organ pipe: $f_n = n\frac{v}{2L}$, $n=1,2,3,\dots$ (all harmonics present).
• For a closed organ pipe: $f_n = n\frac{v}{4L}$, $n=1,3,5,\dots$ (only odd harmonics).

Supplementary reference (not an NCERT-numbered table) -- physical quantities used in this chapter: symbol, dimensions, SI unit, and remarks for wavelength, propagation constant, wave speed, and beat frequency …