What went wrong when the king rode under the arch?

It was too low and knocked off his crown

How does the chain of blame unfold in the poem?

Each accused person blames another, ending with the king's own changes

Distinguish transverse and longitudinal waves.

In a transverse wave particles move perpendicular to the direction of propagation; in a longitudinal wave they move along it, as in sound.

Write the equation of a travelling harmonic wave.

\(y(x,t)=A\sin(kx-\omega t+\phi)\), with angular wavenumber \(k=2\pi/\lambda\) and angular frequency \(\omega=2\pi\nu\).

Write the speed of a transverse wave on a stretched string.

\(v=\sqrt{\dfrac{T}{\mu}}\), where \(T\) is the tension and \(\mu\) the mass per unit length.

Give the Newton-Laplace formula for the speed of sound in a gas.

\(v=\sqrt{\dfrac{\gamma P}{\rho}}\), where \(\gamma\) is the ratio of specific heats — Laplace's adiabatic correction to Newton's formula.

State the principle of superposition of waves.

When two or more waves overlap, the resultant displacement at any point is the algebraic sum of the displacements due to the individual waves.

What are nodes and antinodes in a standing wave?

Nodes are points of zero displacement; antinodes are points of maximum displacement.

How are beats produced and what is the beat frequency?

Beats arise from superposition of two waves of slightly different frequencies; the beat frequency equals the difference of the two frequencies.

What is the Doppler effect?

The apparent change in the observed frequency of a wave due to relative motion between the source and the observer.

Why does sound travel faster in solids than in gases?

Because solids have much greater elastic moduli relative to their density, and wave speed increases with the elasticity-to-density ratio.

Waves

Class 11 Physics · Physics Part II · Chapter 7

163 members in the CBSE community

View all

CBSE Class 11 · Physics

Ch 8–14 formulas and table values, by page

Marks booster + cheatsheet: key concepts in 2 lines each, common traps
20-mark block: Ch 8–12
10-mark block: Oscillations and Waves
Common traps, corrected
7 chapters: every solved-example result
Sound, standing waves and beats covered

Page 1 free about 8 min read, Full kit about 55 min read

₹159See the full kit

CBSE Class 11 · Physics

Every formula of Ch 1–7, with page numbers

Marks booster + cheatsheet: key concepts in 2 lines each, common traps
23-mark block: Ch 1–4
17-mark block: Ch 5–7
Common traps, corrected
7 chapters: every solved-example result
Every unit and dimension, listed

Page 1 free about 8 min read, Full kit about 55 min read

₹159See the full kit

View all 44 amazing Marks Booster kits →

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.

Transverse and longitudinal wavesDisplacement relation for a progressive waveSpeed of a travelling waveSpeed of waves on a string and of soundPrinciple of superposition of wavesStanding waves and normal modesBeatsThe Doppler effect

Key terms

Wave

A disturbance that propagates through a medium carrying energy and information without net transport of matter.

Transverse wave

A wave in which the medium particles oscillate perpendicular to the direction of wave propagation.

Longitudinal wave

A wave in which the medium particles oscillate along the direction of propagation, such as sound in air.

Wavelength

The distance between two consecutive points in the same phase of a wave, related to wavenumber by \(k=2\pi/\lambda\).

Standing wave

A wave pattern formed by superposition of two identical waves travelling in opposite directions, having fixed nodes and antinodes.

Beats

The periodic variation in loudness produced when two waves of slightly different frequencies superpose.

Extra questions & answers

Try one from this chapter

In a transverse wave, the particles of the medium vibrate:

Flashcards & interactive practice