Waves

What is a Wave?

A wave transfers energy from one place to another without transferring matter. The particles (or fields) vibrate as the wave passes, but return to their original positions.

Types of Wave

Transverse Waves

• Vibration (oscillation) is perpendicular (at right angles) to the direction of wave travel
• Examples: all electromagnetic waves (light, radio, X-rays), water surface waves, S-waves (seismic)
• Can travel through a vacuum (EM waves)
• Can be shown on a rope or slinky shaken sideways

Longitudinal Waves

• Vibration is parallel (in the same direction) to the direction of wave travel
• Examples: sound waves, ultrasound, P-waves (seismic)
• Travel as a series of compressions (regions of high pressure) and rarefactions (regions of low pressure)
• Cannot travel through a vacuum (require a medium)

Key Wave Properties

Amplitude A: Maximum displacement from the rest position. Measured in metres (m). Greater amplitude = more energy carried.

Wavelength (λ): Distance between two adjacent points in phase (e.g., crest to crest, or compression to compression). Measured in metres (m).

Frequency (f): Number of complete waves (oscillations) passing a point per second. Measured in hertz (Hz).

Time period (T): Time for one complete wave to pass a point. $$T = rac{1}{f}$$

Wave speed (v): How fast the wave travels through the medium. $$v = flambda$$

Where:

• v = wave speed (m/s)
• f = frequency (Hz)
• λ = wavelength (m)

Worked example: A sound wave has a frequency of 340 Hz and a wavelength of 1 m. Speed = 340 × 1 = 340 m/s (speed of sound in air at room temperature — a useful fact to remember)

Reflection

Reflection occurs when a wave hits a surface and bounces back.

Law of reflection: Angle of incidence = Angle of reflection (both measured from the normal — a line perpendicular to the surface at the point of incidence).

Applications: Mirrors, echo (sound), radar, sonar (ultrasound for depth measurement in the sea).

Echo calculation: $$ ext{distance} = rac{v imes t}{2}$$ (Divide by 2 because the wave travels to the object AND back)

Example: An ultrasound pulse takes 0.4 s to return from the seabed. Speed of sound in water = 1500 m/s. Distance = (1500 × 0.4)/2 = 300 m.

Refraction

Refraction is the change in direction (bending) of a wave when it passes from one medium to another — caused by a change in wave speed.

• Wave travelling into a denser medium (e.g., air → glass): slows down → bends toward the normal
• Wave travelling into a less dense medium (e.g., glass → air): speeds up → bends away from the normal

Key point: Frequency does NOT change during refraction. Speed and wavelength both change.

Snell's Law (Higher Tier): n = sin i / sin r (ratio of sines of incident and refracted angles)

Applications: Lenses (spectacles, cameras), prisms (splitting white light into spectrum), optical fibres (total internal reflection — basis of broadband internet).

WJEC Practical Note

WJEC required practical: investigating reflection and refraction using ray boxes, mirrors and glass blocks. Draw incident ray, reflected/refracted ray, normal; measure angles accurately with a protractor.