Chapter 14 - Waves

When a disturbance travels along a string, through water or through air, it carries energy from one place to another. The material particles usually oscillate around their equilibrium positions instead of travelling with the disturbance over the full distance.

Waves Class 11 studies mechanical waves, their mathematical description, superposition, reflection, standing waves, harmonics and beats.

What is wave motion?

A mechanical wave is a disturbance that travels through a material medium.

Mechanical waves cannot travel through a vacuum because they require particles of a medium to transmit the disturbance.

Important wave quantities include:

• Amplitude

• Wavelength

• Frequency

• Time period

• Wave speed

• Phase

• Angular frequency

• Wave number

Wave speed, frequency and wavelength are related. The frequency is determined by the source, while speed depends on the properties of the medium.

Transverse and longitudinal waves

In a transverse wave, particles oscillate perpendicular to the direction of propagation.

Examples include idealised waves on a stretched string.

In a longitudinal wave, particles oscillate parallel to the direction of propagation. Compressions and rarefactions move through the medium.

Sound in air is a longitudinal mechanical wave.

Progressive waves

A progressive wave travels through the medium and transfers energy.

Students learn the displacement relation for a travelling wave and interpret its amplitude, frequency, wavelength, phase and direction of propagation.

Particle velocity must not be confused with wave velocity. The particles oscillate, while the wave pattern travels.

Principle of superposition

When two or more waves overlap, the resultant displacement equals the algebraic sum of the individual displacements.

Superposition explains interference, standing waves and beats.

Reflection of waves

Waves reflect when they encounter boundaries.

The phase change during reflection depends on the type of boundary. Students compare reflection at fixed and free ends.

Standing waves

Standing waves are formed by the superposition of two identical waves travelling in opposite directions.

They contain:

• Nodes, where displacement remains zero

• Antinodes, where displacement amplitude is maximum

A standing wave does not transfer energy along the medium in the same way as a progressive wave.

Strings and organ pipes

Boundary conditions allow only certain wavelengths and frequencies.

Students study:

• Fundamental mode

• Harmonics

• Standing waves on stretched strings

• Open organ pipes

• Closed organ pipes

An open pipe supports a different sequence of harmonics from a pipe closed at one end.

Beats

Beats are produced when two waves of slightly different frequencies overlap.

The sound intensity rises and falls periodically. Beat frequency equals the difference between the two frequencies.

Common student difficulties

Students frequently:

• Think medium particles travel with the wave

• Confuse particle velocity with wave speed

• Mix wavelength and amplitude

• Confuse nodes with antinodes

• Use string boundary conditions for air columns

• Assume open and closed organ pipes have identical harmonics

• Add frequencies instead of finding their difference for beats

Learning with Teachoo

Teachoo provides wave diagrams, progressive-wave explanations, standing-wave patterns, formulae, NCERT solutions, harmonics questions, beat-frequency numericals and MCQs.

Each solution identifies the type of wave and the applicable boundary conditions before using a formula.

Frequently Asked Questions

What does a wave transfer?

A wave transfers energy and momentum. The particles of the medium usually oscillate around their equilibrium positions.

What is the difference between transverse and longitudinal waves?

In transverse waves, particles oscillate perpendicular to propagation. In longitudinal waves, they oscillate parallel to propagation.

What is a standing wave?

It is a stationary pattern formed by two identical waves travelling in opposite directions.

What is the difference between a node and an antinode?

A node has zero displacement amplitude. An antinode has maximum displacement amplitude.

What are beats?

Beats are periodic variations in intensity produced when two waves of slightly different frequencies overlap.