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Science Grade XI Physics

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Text lesson

Chapter 14: Waves

Grade 11 Science | Chapter 14

Waves

Waves carry energy without carrying matter. This chapter covers transverse and longitudinal waves, the wave equation, superposition, standing waves and beats.

Core Concepts

Key Principles

Worked Examples

Practice Sets

Contents

Introduction: What Is a Wave

Types of Waves

Wave Quantities and the Wave Equation

Speed of a Wave

Superposition and Standing Waves

Beats

Key Reasoning (Principles)

Worked Examples (10)

Practice Sets A to D

10.

Summary and Exam Quick-Check

1. Introduction: What Is a Wave

A wave is a disturbance that travels through a medium or space, carrying energy from one place to another without carrying the matter along with it. Sound, light and ripples on water are all waves. This chapter classifies waves, defines the quantities that describe them, and studies what happens when waves meet.

Core idea

A wave transfers energy, not matter. Its speed, frequency and wavelength are linked by v = f λ, and when waves overlap they add by superposition, giving standing waves and beats.

2. Types of Waves

In a transverse wave the particles of the medium vibrate at right angles to the direction the wave travels, as on a string or with light. In a longitudinal wave they vibrate along the direction of travel, forming compressions and rarefactions, as with sound. Both transfer energy through the medium without moving it along permanently.

Diagram 1 – Transverse and Longitudinal Waves

A transverse wave with vibration across the travel and a longitudinal wave with vibration along it

Fig 1. In a transverse wave the medium vibrates across the direction of travel; in a longitudinal wave it vibrates along it, as compressions and rarefactions.

3. Wave Quantities and the Wave Equation

A wave is described by its wavelength λ, the distance between successive identical points; its frequency f, the number of waves per second; its period T = 1 ÷ f; and its amplitude. These are linked by the wave equation v = f λ: the speed equals the frequency times the wavelength.

4. Speed of a Wave

The speed of a wave depends on the medium. On a stretched string the speed is the square root of (T ÷ μ), where T is the tension and μ the mass per unit length, so a tighter or lighter string carries waves faster. Sound travels faster in solids than in gases. In any one medium, the speed is fixed, so a higher frequency means a shorter wavelength.

5. Superposition and Standing Waves

When two waves meet, the principle of superposition says the total displacement is the sum of the separate displacements. When two equal waves travel in opposite directions, they form a standing wave with fixed nodes that do not move and antinodes that vibrate most. Standing waves on strings and in air columns produce the notes of musical instruments.

Diagram 2 – Standing Wave on a String

A standing wave on a string showing nodes and antinodes

Fig 2. A standing wave has nodes that stay still and antinodes that vibrate with the greatest amplitude, formed by two waves travelling in opposite directions.

6. Beats

When two sound waves of slightly different frequencies overlap, they alternately reinforce and cancel, producing a slow throbbing called beats. The beat frequency equals the difference between the two frequencies. Musicians use beats to tune instruments, listening for the throbbing to disappear when two notes match.

7. Key Reasoning (Principles)

Principle 1: A wave carries energy, not matter

The medium vibrates about fixed positions while the disturbance, and the energy it carries, moves on through it.

Principle 2: Speed, frequency and wavelength are linked

Through v = f λ, a fixed wave speed in a medium means a higher frequency must have a shorter wavelength.

Principle 3: Overlapping waves add by superposition

Where waves meet, their displacements add. This gives standing waves from opposing waves and beats from close frequencies.

8. Worked Examples

Example 1

Q: A wave has frequency 50 Hz and wavelength 4 m. Find its speed.

▶ Show Solution

v = f λ = 50 × 4.

= 200 m/s.

Answer: 200 m/s.

Example 2

Q: A wave travels at 340 m/s with wavelength 2 m. Find its frequency.

▶ Show Solution

f = v ÷ λ = 340 ÷ 2.

= 170 Hz.

Answer: 170 Hz.

Example 3

Q: Find the wavelength of a 256 Hz sound in air (v = 340 m/s).

▶ Show Solution

λ = v ÷ f = 340 ÷ 256.

≈ 1.33 m.

Answer: About 1.33 m.

Example 4

Q: Two tuning forks of 256 Hz and 260 Hz are sounded. Find the beat frequency.

▶ Show Solution

Beat frequency = difference = 260 minus 256.

= 4 Hz.

Answer: 4 Hz.

Example 5

Q: A wave has period 0.02 s. Find its frequency.

▶ Show Solution

f = 1 ÷ T = 1 ÷ 0.02.

= 50 Hz.

Answer: 50 Hz.

Example 6

Q: In a transverse wave, in what direction do the particles vibrate?

▶ Show Solution

At right angles to the direction the wave travels.

Answer: At right angles to the travel.

Example 7

Q: Find the speed of a wave on a string with tension 100 N and μ = 0.01 kg/m.

▶ Show Solution

v = √(T ÷ μ) = √(100 ÷ 0.01) = √10000.

= 100 m/s.

Answer: 100 m/s.

Example 8

Q: A point on a standing wave that never moves is called a:

▶ Show Solution

A point of zero displacement on a standing wave is a node.

Answer: Node.

Example 9

Q: Find the wavelength of a 100 Hz wave travelling at 300 m/s.

▶ Show Solution

λ = v ÷ f = 300 ÷ 100.

= 3 m.

Answer: 3 m.

Example 10

Q: Two notes give 5 beats per second; one is 440 Hz. Find the possible other frequency.

▶ Show Solution

Beat frequency = difference = 5, so the other is 440 plus or minus 5.

Answer: 435 Hz or 445 Hz.

9. Practice Sets A to D

Set A – Multiple Choice (Basic)

1. The wave equation is: (a) v = f ÷ λ (b) v = f λ (c) v = λ ÷ f (d) f = v λ

2. Sound is a wave that is: (a) transverse (b) longitudinal (c) standing (d) electromagnetic

3. A point of zero displacement on a standing wave is a: (a) crest (b) node (c) antinode (d) trough

4. Beat frequency equals the: (a) sum of frequencies (b) difference of frequencies (c) average (d) product

5. Wave speed on a string is: (a) √(T/μ) (b) Tμ (c) T + μ (d) μ/T

▶ Reveal Answers

1. (b) v = f λ.

2. (b) longitudinal.

3. (b) node.

4. (b) difference of frequencies.

5. (a) √(T/μ).

Set B – Short Answer (Understanding)

1. State what a wave transfers and what it does not.

2. State the difference between transverse and longitudinal waves.

3. Write the wave equation.

4. State the principle of superposition.

5. What are beats?

▶ Reveal Answers

1. A wave transfers energy but not matter.

2. In a transverse wave the medium vibrates across the travel; in a longitudinal wave it vibrates along it.

3. v = f λ.

4. When waves overlap, the total displacement is the sum of the separate displacements.

5. The slow throbbing heard when two waves of slightly different frequencies overlap.

Set C – Application and Reasoning

1. A wave has frequency 25 Hz and wavelength 8 m. Find its speed.

2. Find the frequency of a 300 m/s wave of wavelength 5 m.

3. Find the beat frequency of 200 Hz and 205 Hz.

4. Find the wave speed for tension 64 N and μ = 0.04 kg/m.

5. Why does a higher frequency mean a shorter wavelength in a given medium?

▶ Reveal Answers

1. v = 25 × 8 = 200 m/s.

2. f = 300 ÷ 5 = 60 Hz.

3. 205 minus 200 = 5 Hz.

4. v = √(64 ÷ 0.04) = √1600 = 40 m/s.

5. Because v = f λ is fixed in a medium, so if f rises, λ must fall.

Set D – Higher Order (Challenge)

1. A string of length 1 m vibrates in its fundamental mode. Find the wavelength.

2. A 500 Hz wave travels at 340 m/s. Find its wavelength and period.

3. Explain how a standing wave forms on a guitar string.

4. Two waves of 330 Hz and 334 Hz overlap. How many beats are heard each second?

5. Explain why sound travels faster in steel than in air.

▶ Reveal Answers

1. In the fundamental mode the string is half a wavelength, so λ = 2 × 1 = 2 m.

2. λ = 340 ÷ 500 = 0.68 m; period = 1 ÷ 500 = 0.002 s.

3. Waves reflect from the fixed ends and overlap with the incoming waves, forming fixed nodes at the ends and a standing pattern.

4. Beat frequency = 334 minus 330 = 4 beats per second.

5. Because steel is far stiffer, the restoring forces are stronger, so the wave speed, which depends on the medium’s stiffness, is much greater.

Chapter Summary

Wave

A disturbance that carries energy, not matter, through a medium or space.

Types

Transverse (vibration across travel) and longitudinal (along travel).

Wave Equation

v = f λ, linking speed, frequency and wavelength.

Wave Speed

On a string, √(T ÷ μ); fixed in a given medium.

Superposition

Overlapping waves add; opposing waves give standing waves with nodes and antinodes.

Beats

Slow throbbing of frequency equal to the difference of two close frequencies.

Quantity

Unit

Symbol

Wave equation

v = f λ

–

String speed

√(T/μ)

m/s

Beat frequency

|f1 minus f2|

8-Point Exam Quick-Check

A wave carries energy, not matter.

Transverse waves vibrate across the travel; longitudinal waves along it.

Wave equation: v = f times wavelength.

Wave speed on a string = square root of (tension over mass per length).

In a given medium, higher frequency means shorter wavelength.

Overlapping waves add by superposition.

Standing waves have fixed nodes and vibrating antinodes.

Beat frequency = difference between two close frequencies.

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Class 11 Physics Chapter 14: Waves, Complete Notes and Practice

This revision guide follows the current NCERT Class 11 Physics syllabus and develops wave motion, covering transverse and longitudinal waves, wavelength, frequency and the wave equation, the speed of a wave on a string, superposition and standing waves with nodes and antinodes, and beats, with two diagrams, ten worked examples and graded practice. Visit SchoolRevise.com to revise, practise and excel.