Ch 11Waves — Class 11 Physics, concept-first.

The previous unit examined how a single particle oscillates about a fixed mean position. Now imagine a whole medium made up of a huge collection of such particles, each connected to its neighbours.

Dropping a stone into a trough of still water produces a disturbance that spreads outward from the point of impact as a set of concentric, ever-widening circular ripples.

Taking a long string and tying one end to a wall, a single sharp jerk given to the free end sends a single, short-lived, bump-like disturbance travelling along the string -- this is called a wave puls…

Striking a tuning fork against a rubber pad sets its two metal prongs vibrating back and forth about their rest (mean) positions.

Three general characteristics hold for wave motion of any kind. First, for a wave to propagate through a medium at all, that medium must possess both inertia (mass, giving it something to accelerate a…

Waves can first be classified by whether they require a physical medium to travel through. A mechanical wave needs a material medium -- solid, liquid, or gas -- in order to propagate, since it is the…

In transverse wave motion, the individual particles that make up the medium oscillate or vibrate about their own fixed mean (equilibrium) positions in a direction that is perpendicular to the directio…

In longitudinal wave motion, the individual particles that make up the medium oscillate or vibrate about their own fixed mean (equilibrium) positions in a direction that is parallel to the direction t…

Before wave motion can be analysed with any precision, a set of exact defining terms is needed, since simply calling two different wave patterns both "waves" says nothing about how they actually diffe…

Everyday experience shows that wave velocity is not a universal constant but depends entirely on the medium a wave is travelling through.

The speed of a transverse wave travelling along a stretched string can be derived by applying Newton's second law to a tiny curved element of the string as a wave pulse passes through it.

For a longitudinal wave travelling through an elastic medium -- taking air held inside a long cylindrical tube of cross-sectional area as the concrete case -- the wave speed can again be derived from…

Since sound waves are longitudinal, their propagation through air always involves the formation of compressions and rarefactions exactly as described earlier for a vibrating tuning fork.

Sir Isaac Newton assumed that when sound propagates through air, the compressions and rarefactions form slowly enough that any heat generated during compression, and any heat lost during rarefaction,…

In 1816, Laplace resolved the roughly 16% gap between Newton's isothermal prediction and the experimentally observed speed of sound by pointing out a flaw in Newton's underlying assumption.

Rewriting the Laplace speed-of-sound formula using the ideal gas equation of state, (with the number of moles, the universal gas constant), and substituting (with the molar mass) gives the fully expli…

When a sound wave travelling through one medium meets a boundary with a second medium, one of two things can happen: reflection, in which the medium at the boundary is dense/rigid enough that the soun…

Sound waves reflect off a plane (flat) wall in a manner that exactly parallels how light reflects off a plane mirror.

Sound reflected from a curved surface behaves quite differently depending on whether the surface curves outward (convex) or inward (concave).

Four everyday and technological applications rest directly on the reflection of sound waves. The stethoscope works by exploiting multiple successive reflections of sound: it consists of a small disc-s…

A wave that continues propagating through a medium in an ongoing, repeated fashion -- rather than a single isolated pulse -- is called a progressive wave or a travelling wave.

Six properties together characterise any progressive (travelling) wave. First, every particle in the medium vibrates about its own mean (equilibrium) position, and every particle shares the same ampli…

If a wave pulse has shape at the initial instant , and this shape travels rightward along the positive x-direction at a constant speed without changing its form, then at any later time the identical s…

A sinusoidal progressive wave can be visualised using two complementary types of graph, each obtained by holding one of the two independent variables (position or time) fixed while plotting displaceme…

Two distinct velocities arise in describing a progressive wave, and confusing them is one of the most common conceptual errors students make.

When two persons hold opposite ends of a stretched string and each gives a simultaneous jerk, the two resulting wave pulses travel toward each other, meet, and pass through one another, each pulse aft…

The principle of superposition states that the net displacement produced when two or more waves overlap is simply the algebraic sum of their individual displacements, , since the wave equation is line…

When two sound waves of only very slightly different frequencies and (but comparable, equal amplitude) are superposed at a fixed point, the listener perceives not two separate steady tones but a singl…

Whenever a travelling wave reaches a rigid boundary, it reflects back into the medium and interferes there with the still-arriving incident wave; if the incident and reflected waves happen to have exa…

When a wave travelling in one direction along a string meets a rigid boundary, it reflects back into the original medium and interferes there with the wave still arriving from behind it.

Five general characteristics distinguish a stationary (standing) wave from an ordinary progressive (travelling) wave.

A sonometer (the name reflecting its purpose of making sound-related measurements) is a laboratory device built specifically to demonstrate, and let students experimentally verify, the precise relatio…

Clamping a string rigidly at both its ends, at and , and setting it vibrating (as when a guitar string is plucked) can only produce standing waves whose displacement is forced to vanish at both bounda…

Three separate experimental laws describe how the fundamental frequency of a stretched string responds to changing exactly one of its three controlling physical variables -- vibrating length, tension,…

Two sounds can carry exactly the same measurable physical energy and yet be judged very differently "loud" by two different listeners, or by the same listener in two different surroundings -- the soun…

Consider a sound source together with two separate listeners standing at different distances from it: the total sound energy emitted by the source is the same regardless of who measures it or from whe…

Two sounds of exactly the same measured intensity need not be perceived as equally loud. The sound of a balloon bursting inside a silent, closed room, for example, is perceived as very loud, whereas t…

The human ear is capable of detecting an extraordinarily wide range of sound intensities, from as low as about up to about at the threshold of pain (and, more precisely, the threshold of hearing itsel…

Musical wind instruments such as the flute, the clarinet, and the nathaswaram all work on the same underlying principle: setting up standing (stationary) longitudinal sound waves inside a confined col…

The resonance air column apparatus is one of the simplest and most widely used laboratory techniques for experimentally measuring the speed of sound in air at room temperature, and it can also be used…

Standing on a railway platform and listening to the whistle of an approaching, then departing, train reveals a striking effect: the pitch (frequency) heard while the train approaches is noticeably hig…

A wave is a disturbance which carries energy and momentum from one point in space to another point in space without the transfer of the medium; mechanical waves require a medium for their propagation,…

This Evaluation section closes the unit with four kinds of graded practice, mirroring the exact structure printed in the textbook: Part I gathers fifteen multiple choice questions (each with four opti…

Sample papers and previous-year board questions for this subject.