Describing a wave: amplitude, wavelength, frequency and period

What a wave is

• A wave is a disturbance that transfers energy from one place to another without transferring matter.
• The particles of the medium oscillate about a fixed position — they do not travel along with the wave.
  • A duck on the sea bobs up and down as waves pass; it is not carried to the beach.
• Waves need a source that vibrates, and most need a medium to travel through.

Transverse and longitudinal waves

• Transverse — the particles vibrate at right angles to the direction the wave travels.
  • Examples: water waves, waves on a rope or spring, light and all electromagnetic waves.
  • They have crests (highest points) and troughs (lowest points).
• Longitudinal — the particles vibrate along the direction the wave travels.
  • Example: sound (not assessed in this standard, but useful for the contrast).
  • They have compressions (particles bunched together) and rarefactions (particles spread apart).

Drag the controls below to compare the two types — watch how the particles move relative to the direction of travel:

The four quantities that describe a wave

Amplitude ($A$) — the maximum distance a particle moves from its rest position.

• Measured in metres (m).
• Measured from the middle to a crest, not from trough to crest.
• Bigger amplitude means the wave carries more energy.

Wavelength ($\lambda$, "lambda") — the length of one complete wave.

• Measured in metres (m).
• Measure it from any point to the identical point on the next wave: crest to crest, trough to trough, or between two points in step.

Frequency ($f$) — the number of complete waves passing a point each second.

• Measured in hertz (Hz), where $1$ Hz $=$ one wave per second.
• It is set by the source of the wave and never changes when a wave moves into a new material.

Period ($T$) — the time for one complete wave to pass a point.

• Measured in seconds (s).

• Frequency and period are reciprocals of each other:

$$f = \frac{1}{T} \qquad \text{and} \qquad T = \frac{1}{f}$$

• A wave with a period of $0.25$ s has a frequency of $4.0$ Hz — four waves every second.

Wavefronts and rays

Two ways of drawing the same wave, and exam questions use both:

• A wavefront is a line joining points that are in phase — usually drawn along the crests.
  • Adjacent wavefronts are one wavelength apart, so the spacing of the lines is the wavelength.
  • Closer wavefronts mean a shorter wavelength.
• A ray is an arrow showing the direction the wave travels.
  • Rays are always drawn at right angles to the wavefronts.
• Use wavefronts when a question asks about wavelength or speed changing; use rays when it asks about angles and direction.

In phase and out of phase

• Two points are in phase when they are doing exactly the same thing at the same moment — both at a crest, or both moving upward through the middle.
  • Points one wavelength apart (or any whole number of wavelengths) are in phase.
• Two points are out of phase when they are doing opposite things — one at a crest while the other is at a trough.
  • Points half a wavelength apart are completely out of phase.