Wave Properties
Define amplitude, wavelength, frequency, period, speed, phase, transverse waves, longitudinal waves, and superposition.
A lesson of Physics, in Waves, Sound, and Light, about 10 minutes.
By the end of this lesson, you will be able to define and calculate wave speed, frequency, wavelength, and amplitude; distinguish transverse from longitudinal waves; and apply the wave equation.
What is a Wave?
A wave is a disturbance that transfers energy through a medium (or through space) without permanently displacing the medium.
Mechanical waves: require a medium (sound, water waves, seismic waves).
Electromagnetic waves: do not require a medium; travel through vacuum at speed of light (light, radio waves, X-rays).
Wave Parameters
Wavelength ($\lambda$): distance between two consecutive identical points (crest to crest, trough to trough). Units: meters.
Frequency ($f$): number of complete waves that pass a point per second. Units: Hz = s⁻¹.
Period ($T$): time for one complete wave cycle. $T = 1/f$.
Amplitude ($A$): maximum displacement from equilibrium. Related to energy: $E \propto A^2$.
Wave speed ($v$): how fast the wave pattern moves.
$$v = f\lambda$$
Types of Waves
Transverse waves: displacement perpendicular to direction of propagation.
Examples: light, string waves, seismic S-waves.
Longitudinal waves: displacement parallel to direction of propagation (compressions and rarefactions).
Examples: sound, seismic P-waves, spring waves.
Surface waves: combination of both (water waves, seismic surface waves).
Example 1 — Wave Equation
A water wave has frequency 2.5 Hz and wavelength 0.80 m. Find the wave speed.
$v = f\lambda = 2.5 \times 0.80 = 2.0$ m/s
Example 2 — Finding Wavelength from Speed and Frequency
A sound wave travels at 343 m/s with frequency 440 Hz. Find the wavelength.
$\lambda = v/f = 343/440 = 0.780$ m
Wave Energy and Amplitude
$E \propto A^2$: doubling amplitude → 4× the energy.
$E \propto f^2$ for harmonic oscillators.
Wave intensity: $I = P/A_{\text{area}}$ (power per unit area); decreases as $1/r^2$ for a point source (inverse square law).
Standing Waves
When a wave reflects and interferes with the incoming wave, standing waves form.
Nodes: points of no displacement (destructive interference).