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Physics · Class 11 Science

Ch 14Waves — Class 11 Physics, concept-first.

WBCHSE's Unit 10, "Oscillation and Waves", studies periodic motion in two stages. SUB TOPIC 1 examines simple harmonic motion (SHM) in an isolated oscillating system -- a pendulum, a mass on a spring -- where the disturbance stays confined to that one system.

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Key concepts

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Transverse and Longitudinal Waves

Progressive waves split into two kinds based on how a medium's particles vibrate relative to the wave's own direction of travel.

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In previous exams

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Chapter contents

The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.

13.1

Introduction

WBCHSE's Unit 10, "Oscillation and Waves", studies periodic motion in two stages. SUB TOPIC 1 examines simple harmonic motion (SHM) in an isolated oscillating system -- a pendulum, a mass on a spring…

13.2

Wave Motion: Mechanical Waves and the Need for a Medium

A wave is a disturbance that travels through a medium (or, for electromagnetic waves, through empty space) carrying energy and momentum from one point to another without any net displacement of the me…

13.3

Transverse and Longitudinal Waves

Mechanical waves are classified into two kinds according to the relation between the direction in which the medium's particles vibrate and the direction in which the wave itself propagates.

13.4

Displacement Relation for a Progressive Wave

A progressive (or travelling) wave is one that carries its disturbance steadily onward through the medium, in contrast to the stationary wave met later in this chapter.

13.4.1

Wavelength and Angular Wave Number

The wavelength of a progressive wave is the distance, measured along the direction of propagation, between two nearest points of the medium that are in exactly the same phase of oscillation at a given…

13.4.2

Period, Frequency and Angular Frequency

The period of a progressive wave is the time taken by any one particle of the medium to complete one full cycle of its oscillation, and the frequency is the number of complete oscillations that partic…

13.5

The Speed of a Travelling Wave

It is essential to distinguish the wave speed from the frequency or wavelength individually: while connects the three quantities kinematically, the speed at which a mechanical wave travels through a g…

13.5.1

Speed of a Transverse Wave on a Stretched String

For a transverse wave travelling along a taut string, the elastic (restoring) property is provided by the tension in the string -- it is the tension that pulls a displaced element of the string back t…

13.6

Speed of Sound in a Gaseous Medium: Newton's Formula and Laplace's Correction

Sound travels through a gas such as air as a longitudinal wave, so the relevant elastic property is the gas's bulk modulus (which measures its resistance to compression) and the relevant inertial prop…

13.7

Principle of Superposition of Waves

The principle of superposition of waves states that when two or more waves travel through the same region of a medium simultaneously, the resultant (net) displacement of any particle of the medium, at…

13.8

Reflection of Waves and Formation of Stationary Waves

A travelling wave is reflected whenever it meets a boundary -- a change from one medium to another, or the end of a bounded medium such as a string or an air column.

13.9

Stationary Waves in a Stretched String Fixed at Both Ends: Fundamental Mode and Harmonics

Consider a string of length , rigidly fixed at both ends -- the situation in every stringed instrument and in the standard sonometer experiment.

13.10

Stationary Waves in Organ Pipes: Fundamental Mode and Harmonics

An organ pipe is a tube of air, open at one or both ends, inside which a longitudinal stationary wave can be set up by blowing air across an opening (or over a reed) at one end, exciting the enclosed…

13.10.1

Open Organ Pipe

In a pipe open at both ends, both ends must be displacement antinodes. Since an antinode-to-antinode spacing (like a node-to-node spacing) is , the pipe's length must fit a whole number of half-wavele…

13.10.2

Closed Organ Pipe

In a pipe closed at one end and open at the other, the closed end must be a displacement node while the open end must be a displacement antinode.

13.11

Formation of Beats

When two sound waves of slightly different, but close, frequencies and travel through the same medium and arrive together at a point, their superposition produces a periodic waxing and waning of loudn…

13.12

Doppler Effect of Sound

The Doppler effect is the change in the frequency of a wave as perceived by an observer, occurring whenever there is relative motion between the source of the wave and the observer along the line join…

13.12.1

Source Moving, Observer Stationary

With the observer stationary (), the general Doppler formula reduces to If the source moves TOWARD the stationary observer at speed , the denominator becomes (smaller than ), so -- the observer hears…

13.12.2

Observer Moving, Source Stationary

With the source stationary (), the general Doppler formula reduces to If the observer moves TOWARD the stationary source at speed , then -- a higher pitch is heard, because the moving observer interce…

13.12.3

Both Source and Observer Moving

When both the source and the observer are simultaneously in motion along the line joining them, the two corrections combine into the fully general Doppler formula introduced above, with each of and ca…

Summary

A mechanical wave is a disturbance carrying energy through an elastic, inertial medium without net transport of the medium's own matter; in a transverse wave particles vibrate perpendicular to propaga…

Sample & Board Papers

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

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+Show 8 questions8 questions
  1. Example 1A pulse travels along a stretched horizontal string, and a sound pulse travels along a column of air in a pipe. State, with a reason for eac…Free
  2. Example 2A sonometer wire of length $2\ \text{m}$ has a mass of $5\ \text{g}$ and is stretched with a tension of $80\ \text{N}$. Find the speed of a…Free
  3. Example 3Using Laplace's corrected formula, calculate the speed of sound in air at STP, given the pressure $P=1.013\times10^{5}\ \text{Pa}$, the dens…Free
  4. Example 4A progressive wave travelling along a stretched string is described by $y=0.02\sin(4x-200t)$ (SI units). Find (a) the amplitude, (b) the wav…Preview
  5. Example 5Two sound waves of equal amplitude $3\ \text{cm}$ and the same frequency arrive at a point with a constant phase difference of $60^\circ$. F…Preview
  6. Example 6A string of length $1\ \text{m}$, fixed at both ends, carries transverse waves of speed $200\ \text{m s}^{-1}$. Find the fundamental frequen…Preview
  7. Example 7An organ pipe, open at both ends, has a length of $0.5\ \text{m}$. Taking the speed of sound in air as $340\ \text{m s}^{-1}$, find (a) the…Preview
  8. Example 8A car's horn sounds a note of frequency $500\ \text{Hz}$ as the car moves toward a stationary pedestrian at $20\ \text{m s}^{-1}$. Taking th…Preview
+Show 8 questions8 questions
  1. Q9Distinguish between a progressive (travelling) wave and a stationary (standing) wave, with reference to how each transports energy through t…Free
  2. Q10Starting from the definitions of wavelength and period, derive the relation $v=f\lambda$ connecting a wave's speed, frequency, and wavelengt…Free
  3. Q11State Newton's formula for the speed of sound in a gas and the assumption on which it rests. Explain the physical reasoning behind Laplace's…Free
  4. Q12State the principle of superposition of waves. Using it, explain what is meant by constructive interference and destructive interference, st…Preview
  5. Q13Explain how a stationary wave is formed by the superposition of an incident wave and its own reflected wave. Define the terms node and antin…Preview
  6. Q14A string fixed at both ends and an organ pipe closed at one end are both set into their fundamental mode of vibration. Explain why the strin…Preview
  7. Q15Explain how beats are formed when two sound waves of slightly different frequency are superposed, and derive the expression for the beat fre…Preview
  8. Q16State the general Doppler-effect formula for the frequency heard by an observer when both the source and the observer are in motion, definin…Preview
+Show 8 questions8 questions
  1. Q17A sonometer wire of length $1.5\ \text{m}$ has a mass of $15\ \text{g}$ and is kept under a tension of $300\ \text{N}$. Calculate the speed…Free
  2. Q18Using $P=1.0\times10^{5}\ \text{Pa}$, $\rho=1.293\ \text{kg m}^{-3}$, and $\gamma=1.4$ for air, calculate (a) the speed of sound predicted b…Free
  3. Q19A stretched string of length $0.6\ \text{m}$, fixed at both ends, carries transverse waves at a speed of $240\ \text{m s}^{-1}$. Find the fr…Free
  4. Q20An organ pipe open at both ends has a length of $0.85\ \text{m}$. Taking the speed of sound in air as $340\ \text{m s}^{-1}$, find the funda…Preview
  5. Q21An organ pipe closed at one end has a length of $0.5\ \text{m}$. Taking the speed of sound in air as $340\ \text{m s}^{-1}$, find the fundam…Preview
  6. Q22A tuning fork $A$ of frequency $256\ \text{Hz}$ produces $4$ beats per second when sounded together with another tuning fork $B$ of unknown…Preview
  7. Q23An observer moves toward a stationary source of sound of frequency $400\ \text{Hz}$ at a speed of $15\ \text{m s}^{-1}$. Taking the speed of…Preview
  8. Q24A source of sound of frequency $600\ \text{Hz}$ moves toward a stationary point at $10\ \text{m s}^{-1}$, while an observer at that point mo…Preview