Describing Wave Motion

Wave Motion Basics

Wave motion is the transfer of energy from one point to another without the transfer of matter. It involves a disturbance that moves through a medium, such as air, water, or solids, carrying energy but not particles themselves.

The medium is essential for most waves because it provides the particles that vibrate to pass the energy along. For example, in sound waves, air particles vibrate and pass the energy to neighbouring particles, allowing the wave to travel through the air.

Waves transfer energy by causing particles in the medium to oscillate about a fixed position, but the particles themselves do not travel with the wave.

Types of Waves

Transverse waves have oscillations perpendicular (at right angles) to the direction of energy transfer. The particles move up and down while the wave moves horizontally.

Examples of transverse waves include:

• Waves on a string
• Water waves on the surface of a pond
• Seismic S-waves (secondary waves) in solids

Longitudinal waves have oscillations parallel to the direction of energy transfer. The particles move back and forth in the same direction as the wave.

Examples of longitudinal waves include:

• Sound waves in air
• Ultrasound waves in fluids and solids
• Seismic P-waves (primary waves) in solids

In air and fluids, sound waves are longitudinal because particles compress and rarefy in the direction the wave travels. In solids, both transverse and longitudinal waves can travel because particles are tightly packed and can move in different directions.

Wave Properties

Amplitude is the maximum displacement of a particle from its rest position. It relates to the energy carried by the wave—the larger the amplitude, the more energy the wave transfers.

Wavelength ($\lambda$) is the distance between two points in phase on a wave, such as from crest to crest or compression to compression.

Frequency ($f$) is the number of waves passing a point each second, measured in hertz (Hz).

Period ($T$) is the time taken for one complete wave to pass a point, measured in seconds (s). It is the inverse of frequency:

$$T = \frac{1}{f}$$

The speed of a wave ($v$) depends on its frequency and wavelength, related by:

$$v = f \times \lambda$$

For example, if a sound wave has a frequency of 500 Hz and a wavelength of 0.68 m in air, its speed is:

$$v = 500 \times 0.68 = 340 \text{ m/s}$$

Wave Behaviour

Reflection occurs when a wave bounces back after hitting a boundary between two media. The angle of incidence equals the angle of reflection. Reflection is important in echoes and sonar.

Absorption happens when the wave energy is taken in by the medium or surface, often converting to heat. Soft materials, like curtains or carpets, absorb sound waves, reducing echoes.

Transmission is when waves pass through a medium or boundary. The wave may change speed and direction depending on the new medium; this change in direction is called refraction.

The speed of a wave depends on the medium's properties:

• Sound waves travel fastest in solids, slower in liquids, and slowest in gases because particles are closer together in solids, allowing vibrations to pass more quickly.
• For example, sound travels at about 340 m/s in air, 1500 m/s in water, and even faster in steel (~5000 m/s).

For instance, a wave with frequency 20 Hz and wavelength 2 m has a speed of $v = 20 \times 2 = 40 \text{ m/s}$.