# TYPES OF WAVES

## Progressive Waves

A progressive wave is one which transfers energy (NOT matter) during propagation. Progressive waves include two (2) types of waves: transverse and longitudinal waves.

## Longitudinal Waves

Longitudinal waves are waves in which the direction of vibration of the particles is parallel to (i.e. along) the direction of wave propagation i.e. the particles of the medium vibrate along the same direction in which the wave travels. Longitudinal waves can be observed on a slinky resting on a surface with one end fixed and the other pulled and released. This generates a series of compressions and rarefactions which travel along the slinky as the wave propagates.

### Longitudinal Waves in a Slinky

Direction of vibration = Direction of wave propagation

[insert PICTURE 4-1]

R: Rarefaction – coils are pulled apart (displacement great and positive)

C: Compression – coils are pushed together (displacement great and negative)

Longitudinal waves therefore appear as a series of compressions and rarefactions.

Longitudinal waves include sound waves. Sound waves compress the air as they move forward, then move back before creating another compression.

The air molecules vibrate to and fro as the sound wave propagates but on average remain undisplaced.

## Transverse Waves

Transverse waves are waves in which the direction of vibration of the particles of the medium is perpendicular (i.e. at right angles to the direction of wave propagation).

A single particle of a medium through which a transverse wave is transported is shown below:

Direction of particle vibration is PERPENDICULAR to direction of wave propagation

[insert PICTURE 4-2]

A transverse wave can be observed on a horizontally stretched slinky, with both ends fixed, which is given a vertical displacement.

As the coils oscillate vertically, the wave propagates horizontally.

A transverse wave can also be observed in a rope in which one end is given a continuous vertical displacement.

The wave form of a transverse wave appears as a series of crests (peaks) and troughs (valleys).

[insert PICTURE 4-3]                                                           Displacement position

C – crest, T – trough

A transverse wave may be regarded as an actual snapshot of the medium through which it travels.

Transverse waves include water waves and electromagnetic waves (i.e. microwaves, radio waves, infra-red, visible light, UV, x-rays and γ-rays).

Transverse waves are characterized by partial motion being perpendicular to wave motion.

### Graphs of Progressive Waves

The displacement of a progressive wave varies simultaneously with both time and space (i.e. position).

If either (time or space) is assumed fixed, then a graph showing how the displacement varies with the other can be obtained.

#### Displacement-Position Graph

The displacement-position graph of a progressive wave can be obtained when time is assumed to be fixed, i.e. at an instant.

[insert PICTURE 4-4]

A – amplitude, λ – wavelength

The displacement-position graph looks the same for both transverse and longitudinal waves.

The only difference is that the displacement of the particles in a longitudinal wave is parallel to the direction of propagation, whereas the displacement of the particles in a transverse wave is perpendicular to the direction of wave propagation.

#### Displacement-Time Graph

The displacement-time graph of a progressive wave can be obtained only at a fixed position in space, i.e. at a point.

[insert PICTURE 4-5]

T – period, A – amplitude