This note covers what waves are, how to describe them using amplitude, wavelength, frequency and speed, and how they behave when they reflect, refract or diffract. Water waves in a ripple tank are used as the standard example, and the same ideas apply to light and sound.
Key ideas
What a wave does. A wave transfers energy from one place to another without transferring matter. A cork on the sea bobs up and down as waves pass, but it does not travel with the wave. Waves are produced by vibrations (oscillations) of a source.
Two types of wave.
- Transverse: the vibrations are at right angles to the direction the wave travels. Examples: water waves, light and all other electromagnetic waves, waves on a rope.
- Longitudinal: the vibrations are parallel to the direction the wave travels. The wave is a series of compressions (particles squashed together) and rarefactions (particles spread apart). Example: sound.
Describing a wave.
- Amplitude: the maximum displacement of a point on the wave from its rest position.
- Wavelength (λ): the distance between two matching points on neighbouring waves, for example crest to crest. Measured in metres.
- Frequency (f): the number of complete waves passing a point each second. Measured in hertz (Hz).
- Period (T): the time for one complete wave to pass a point. T = 1 ÷ f. Measured in seconds.
- Wavefront: a line joining points on a wave that are moving in step, such as the crest line of a ripple.
- Wave speed (v): the distance the wave travels each second.
These are linked by the wave equation: v = f λ. When a wave changes speed, its frequency stays the same because the source sets the frequency. Only the wavelength changes.
Reflection. A wave bounces off a barrier. For a straight barrier, the angle of incidence equals the angle of reflection. Both angles are measured from the normal, which is a line drawn at 90° to the surface where the wave hits. Reflected waves keep the same speed, frequency and wavelength.
Refraction. When a wave moves from one medium into another, its speed changes. If the wave hits the boundary at an angle, it also changes direction. In a ripple tank, waves move more slowly in shallow water than in deep water.
- Going into a slower region: the wavelength shortens, the wavefronts bunch up and the wave bends towards the normal.
- Going into a faster region: the wavelength lengthens and the wave bends away from the normal.
- Along the normal (hitting the boundary at 90°): the speed and wavelength change but the direction does not.
- The frequency never changes.
Diffraction. Diffraction is the spreading out of waves as they pass through a gap or go around the edge of an obstacle.
- The effect is greatest when the gap is about the same size as the wavelength.
- A gap much wider than the wavelength gives little spreading, with only the edges curving.
- A narrower gap, or a longer wavelength, gives more spreading.
- The wavelength, frequency and speed do not change during diffraction.
This explains why you can hear someone talking around a corner. Sound has a wavelength of the order of metres, which is similar to the size of doorways, so it diffracts well. Light has a very small wavelength, so it appears to travel in straight lines past everyday objects.
Definitions and formulae
| Term or formula | Meaning / when to use |
|---|---|
| Transverse wave | Oscillations are perpendicular to the direction of travel of the wave. |
| Longitudinal wave | Oscillations are parallel to the direction of travel. Made of compressions and rarefactions. |
| Amplitude | Maximum displacement from the rest position. |
| Wavelength λ | Distance between matching points on adjacent waves (m). |
| Frequency f | Waves per second (Hz). |
| T = 1 ÷ f | Converts between period (s) and frequency (Hz). |
| v = f λ | Wave speed (m/s) from frequency (Hz) and wavelength (m). |
| Reflection | Angle of incidence = angle of reflection, both measured from the normal. |
| Refraction | Change of speed (and usually direction) of a wave at a boundary between media. Frequency unchanged. |
| Diffraction | Spreading of a wave at a gap or edge. Largest when gap size is about one wavelength. |
Worked examples
Example 1 A vibrating bar produces water waves of frequency 5.0 Hz in a ripple tank. The distance between neighbouring crests is 0.30 m. Find (a) the period of the waves and (b) their speed.
(a) T = 1 ÷ f = 1 ÷ 5.0 = 0.20 s.
(b) v = f λ = 5.0 × 0.30 = 1.5 m/s.
Answer: (a) 0.20 s; (b) 1.5 m/s
Example 2 Ripples of frequency 4.0 Hz travel from deep water at 0.60 m/s into shallow water, where their speed falls to 0.40 m/s. Find the wavelength in each region and state what happens to the frequency.
The frequency is set by the source and does not change: it stays at 4.0 Hz.
Deep water: λ = v ÷ f = 0.60 ÷ 4.0 = 0.15 m.
Shallow water: λ = v ÷ f = 0.40 ÷ 4.0 = 0.10 m.
Answer: 0.15 m in deep water, 0.10 m in shallow water; the frequency stays 4.0 Hz.
Example 3 A straight water wave hits a flat barrier. The wave travels at 35° to the barrier surface (the angle between the ray and the barrier is 35°). Find the angle of incidence and the angle of reflection.
Angles of incidence and reflection are measured from the normal, which is at 90° to the barrier.
Angle of incidence = 90 − 35 = 55°.
Angle of reflection = angle of incidence = 55°.
Answer: both angles are 55°
Common errors
- Common error: measuring the angle of incidence or reflection from the surface of the mirror or barrier. Always measure from the normal.
- Common error: saying the frequency changes when a wave refracts. Speed and wavelength change, but the frequency does not.
- Common error: saying waves carry matter along with them. Only energy is transferred.
- Common error: saying that more diffraction happens through a wider gap. Diffraction is greatest when the gap is about the same size as the wavelength, and a narrower gap spreads waves more.
- Common error: reading the amplitude as the full height from crest to trough. Amplitude is measured from the rest position to a crest (or trough).
Exam tip: In wave calculations, check units first. Convert kHz, cm or ms to Hz, m or s before you substitute into v = f λ.
Check yourself
- A wave has a frequency of 250 Hz and a wavelength of 1.32 m. What is its speed?
Answer
v = f λ = 250 × 1.32 = 330 m/s. - Ten complete waves pass a point in 4.0 s. Find the frequency and period.
Answer
f = 10 ÷ 4.0 = 2.5 Hz. T = 1 ÷ 2.5 = 0.40 s. - Give one difference between a transverse and a longitudinal wave, and one example of each.
Answer
In a transverse wave the vibrations are at right angles to the direction of travel (light, water waves). In a longitudinal wave the vibrations are along the direction of travel (sound). - Waves of wavelength 2.0 cm travel towards a gap of width 2.0 cm and then towards a gap of width 20 cm. Which gap produces more diffraction and why?
Answer
The 2.0 cm gap. Diffraction is greatest when the gap is about the same size as the wavelength. Through the 20 cm gap the waves mostly continue straight on.