CBSE Class 11 — Notes, Chapters & Practice Quizzes

Chapter 7: Waves

Summary

A wave is a disturbance that travels through a medium transporting energy and information without the bulk transport of matter, as seen when a pebble disturbs still water or when sound moves through air. In a transverse wave the medium particles vibrate perpendicular to the direction of propagation, while in a longitudinal wave they vibrate along it; sound in air is longitudinal. A travelling harmonic wave is described by \(y(x,t)=A\sin(kx-\omega t+\phi)\), where \(A\) is amplitude, \(k=2\pi/\lambda\) the angular wavenumber and \(\omega=2\pi\nu\) the angular frequency; the wave speed is \(v=\nu\lambda=\omega/k\). The speed of a transverse wave on a stretched string is \(\sqrt{T/\mu}\), and the speed of sound in a medium depends on its elasticity and density (Newton's formula corrected by Laplace gives \(\sqrt{\gamma P/\rho}\) for a gas). When two waves overlap, the principle of superposition gives a resultant displacement equal to the sum; this leads to interference, to standing waves with nodes and antinodes on strings and in air columns producing harmonics, and to beats when two slightly different frequencies combine. The Doppler effect describes the change in observed frequency due to relative motion of source and observer.

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