Home/Waves

Waves & Sound

Understanding wave properties, superposition, and the Doppler effect.

Wave Properties

A wave transfers energy through a medium without transferring matter.

Amplitude (A)
Maximum displacement from equilibrium
meters
Wavelength (λ)
Distance between two identical points
meters
Period (T)
Time for one complete cycle
seconds
Frequency (f)
Number of cycles per second
Hz
Wave Speed (v)
Speed of wave propagation
m/s
Phase (φ)
Position in the cycle
radians

Core Formulas

Wave Speed

v = fλ

Speed = frequency × wavelength

Period & Frequency

T = 1/f    f = 1/T

Wave Equation

y(x,t) = A·sin(kx − ωt)

k = 2π/λ (wave number), ω = 2πf (angular freq.)

Superposition & Interference

When two waves overlap, their displacements add (superposition principle).

Constructive Interference

Waves in phase (Δφ = 0, 2π, 4π...) — amplitudes add.

A_result = A₁ + A₂

Destructive Interference

Waves out of phase (Δφ = π, 3π...) — amplitudes cancel.

A_result = |A₁ − A₂|

Doppler Effect

The perceived frequency changes when source or observer are moving relative to each other.

f_obs = f_s × (v + v_obs) / (v − v_source)

Moving toward each other → higher frequency. Moving apart → lower frequency.

Ready to Practice?

Start Practicing →