In this section we describe the main features of a wave and the relationships between them. Understanding these terms is essential for solving problems involving wave motion.
Key Terms and Definitions
Wavefront – an imaginary line (or surface in three dimensions) joining points that are in the same phase of vibration. For a transverse wave the wavefront is perpendicular to the direction of propagation.
Wavelength (\$\lambda\$) – the distance between two consecutive points that are in phase, e.g., crest to crest or trough to trough.
Frequency (\$f\$) – the number of complete cycles that pass a given point per second. Measured in hertz (Hz).
Period (\$T\$) – the time taken for one complete cycle. \$T = \dfrac{1}{f}\$.
Crest (Peak) – the highest point of a transverse wave.
Trough – the lowest point of a transverse wave.
Amplitude (\$A\$) – the maximum displacement of the medium from its equilibrium position. For a transverse wave it is the distance from the equilibrium line to a crest (or trough).
Wave speed (\$v\$) – the rate at which the wave propagates through the medium.
Relationships Between Wave Quantities
The fundamental relationship linking wave speed, frequency and wavelength is:
\$v = f \lambda\$
Where:
\$v\$ = wave speed (m s⁻¹)
\$f\$ = frequency (Hz)
\$\lambda\$ = wavelength (m)
Table of Wave Features
Feature
Symbol
Definition
Units
Wavefront
—
Line joining points of equal phase, perpendicular to direction of travel
—
Wavelength
\$\lambda\$
Distance between successive crests (or troughs)
metre (m)
Frequency
\$f\$
Number of cycles per second passing a point
hertz (Hz)
Period
\$T\$
Time for one complete cycle
second (s)
Crest (Peak)
—
Highest point of a transverse wave
—
Trough
—
Lowest point of a transverse wave
—
Amplitude
\$A\$
Maximum displacement from equilibrium
metre (m) or other appropriate unit
Wave speed
\$v\$
Rate of propagation of the wave through the medium
metre per second (m s⁻¹)
Example Calculation
Suppose a wave has a frequency of 50 Hz and a wavelength of 0.2 m. Its speed is:
Suggested diagram: A transverse wave showing a wavefront, crest, trough, wavelength (\$\lambda\$), amplitude (\$A\$) and the direction of propagation.
Common Misconceptions
Confusing wavelength with amplitude – wavelength is the distance between successive identical points, while amplitude is the height of the wave.
Assuming wave speed changes with frequency – in a given medium, \$v\$ is constant; changing \$f\$ changes \$\lambda\$ accordingly.
Thinking a wavefront is a physical object – it is an imaginary line used to describe the phase of the wave.
Summary
A wave is characterised by its wavefront, wavelength, frequency (or period), amplitude, and speed. The relationship \$v = f\lambda\$ links the three fundamental quantities and is central to solving most wave problems in the IGCSE syllabus.