What is covered in Grade 10 Physical Sciences Longitudinal Waves?

In a longitudinal wave, the particles of the medium move parallel to the direction of wave propagation. Compressions are regions of high pressure; rarefactions are regions of low pressure. Sound waves are longitudinal.

What is Longitudinal wave in Physical Sciences?

A wave in which the disturbance (of particles of the medium) is parallel to the direction of motion of the wave.

The region of high pressure in a longitudinal wave.

What is the formula for Wave equation (longitudinal)?

The formula for Wave equation (longitudinal) is: v = fλ. Where: v = speed (m·s⁻¹), f = frequency (Hz), λ = wavelength (m) The SI unit is m·s⁻¹.

Is Grade 10 Physical Sciences Longitudinal Waves on the CAPS curriculum?

Yes. Longitudinal Waves is part of the official CAPS Physical Sciences curriculum for Grade 10, Term 1 in South Africa. The content on MathSciBuddy follows the Annual Teaching Plan (ATP) set by the Department of Basic Education.

Longitudinal Wave

Not all waves are transverse. In a longitudinal wave, the particles move parallel to the direction the wave travels — not perpendicular. Sound is the most important example of a longitudinal wave in everyday life.

Week 2

3.1 What is a Longitudinal Wave?

Define a longitudinal wave.Draw a diagram to represent a longitudinal wave in a spring, showing the direction of motion of the wave relative to the direction in which the particles move.Define the wavelength and amplitude of a longitudinal wave.Define a compression and a rarefaction.Differentiate between longitudinal and transverse waves.

In a transverse wave, particles move at RIGHT ANGLES to the wave direction. In a longitudinal wave, particles move ALONG THE SAME DIRECTION as the wave. Imagine pushing and pulling the end of a slinky back and forth (instead of sideways). The coils bunch up (compressions) and spread out (rarefactions) and this pattern travels along the slinky — that is a longitudinal wave.

Definition

Longitudinal wave

A longitudinal wave is a wave where the particles in the medium move parallel to the direction of propagation of the wave.

Figure 3.1 — A longitudinal wave in a spring. The particles (coils) move back and forth (←→) in the SAME direction as the wave travels (→). Regions where coils are closest together are called compressions (C); regions where coils are furthest apart are called rarefactions (R). The wavelength λ is the distance from one compression to the next compression.

Definition

Compression

A compression is a region in a longitudinal wave where the particles are closest together.

Definition

Rarefaction

A rarefaction is a region in a longitudinal wave where the particles are furthest apart.

WAVELENGTH OF A LONGITUDINAL WAVE: Just as in a transverse wave, the wavelength (λ) is the distance between two adjacent in-phase points. For a longitudinal wave this means: compression to compression, OR rarefaction to rarefaction (the next one). Both give the same value of λ.

ℹ

Note

AMPLITUDE OF A LONGITUDINAL WAVE: The amplitude is the maximum displacement of a particle from its equilibrium (rest) position. In a longitudinal wave this is a horizontal displacement (back-and-forth movement), not a vertical height.

Transverse vs Longitudinal Waves

Property	Transverse Wave	Longitudinal Wave
Particle motion	PERPENDICULAR to wave direction (up/down)	PARALLEL to wave direction (back/forth)
Pattern seen	Crests and troughs	Compressions and rarefactions
Wavelength (λ)	Crest to next crest (or trough to trough)	Compression to next compression (or rarefaction to rarefaction)
Common examples	Light, water surface waves, waves on a rope	Sound, a pushed slinky
Can it travel in a vacuum?	Yes (light and all EM waves can)	No (needs a material medium — particles must be present)

Figure 3.2 — Comparison of transverse (top) and longitudinal (bottom) waves. In both cases the wave travels to the right. In the transverse wave, particles oscillate up and down. In the longitudinal wave, particles oscillate left and right (back and forth).

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Real World

EVERYDAY EXAMPLE: Tap the end of a metal rod. The vibration travels along the rod as a longitudinal wave — the atoms of the rod compress and expand back and forth along the rod's length. Sound in air is also longitudinal: the air molecules are pushed together (compressions) and pulled apart (rarefactions) as sound travels.

Practice Question

A longitudinal wave in a slinky has a wavelength of 0,8 m. (a) Define a compression and a rarefaction. (b) What is the distance from one compression to the next rarefaction? (c) How does the direction of particle motion in this wave compare to the direction of wave propagation?

(6 marks)