Wave Properties — Wavelength, Frequency, Amplitude

All waves share common properties. Wavelength is the length of one complete wave cycle, frequency is the number of waves per second, and amplitude is the maximum displacement from rest. These properties are related by the wave speed equation v = fλ.

Types of Waves

Type	Direction of vibration	Examples
Transverse	Perpendicular to direction of travel	Light, water waves, EM waves
Longitudinal	Parallel to direction of travel	Sound

Key Wave Properties

Amplitude (A)

The maximum displacement from the rest (equilibrium) position.

A larger amplitude = more energy carried by the wave. For sound: larger amplitude = louder. For light: larger amplitude = brighter.

Wavelength (λ — lambda)

The length of one complete wave cycle — from one crest to the next (or trough to trough).

Measured in metres (m).

Frequency (f)

The number of complete waves passing a point per second.

Measured in hertz (Hz). 1 Hz = 1 wave per second. For sound: higher frequency = higher pitch.

Period (T)

The time for one complete wave cycle.

$T = \frac{1}{f}$

If frequency = 50 Hz → period = 1/50 = 0.02 s

The Wave Speed Equation

$v = f \lambda$

where:

$v$ = wave speed (m/s)
$f$ = frequency (Hz)
$\lambda$ = wavelength (m)

Wave Speed Calculation

A wave has a frequency of 200 Hz and a wavelength of 1.5 m. Find its speed.

$v = f \lambda = 200 \times 1.5 = 300 \text{ m/s}$

Real world: Guitar strings and musical pitch

When you pluck a guitar string, it vibrates and creates a sound wave. A shorter or tighter string vibrates at a higher frequency — producing a higher pitch note. The loudness of the note depends on how hard you pluck (amplitude). Tuning a guitar means adjusting string tension until the frequency matches the correct musical note (e.g. 440 Hz for the note A).

Real world: Radio station frequencies

Radio stations broadcast at different frequencies. A station at "100 FM" broadcasts at 100 MHz (100 million Hz). The speed of all EM waves is c = 3 × 10⁸ m/s, so the wavelength is λ = c/f = (3 × 10⁸) / (100 × 10⁶) = 3 m. That's why radio masts are several metres tall — to efficiently transmit waves of that wavelength.

Real world: Ocean waves reaching a beach

Ocean waves are transverse waves — the water surface moves up and down (perpendicular to the wave's direction of travel toward shore). After a storm far out at sea, waves with long wavelengths (low frequency) travel quickly and arrive at the beach hours before shorter-wavelength waves — which is why surfers feel "swell" before a storm arrives.

Tip Where do you see this in real life? Guitar strings, radio broadcasts, ocean waves, noise-cancelling headphones, and Wi-Fi signals — all involve the properties of waves: amplitude, frequency, and wavelength!

Practice Problems

A sound wave has a speed of 340 m/s and a wavelength of 0.85 m. What is its frequency?

Show answer

f = v/λ = 340/0.85 = 400 Hz.

What happens to the wavelength of a wave if its frequency doubles (speed stays the same)?

Show answer

The wavelength halves. Since v = fλ and v is constant, if f doubles, λ must halve.

Is sound a transverse or longitudinal wave? Explain.

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Longitudinal. Sound waves cause particles to vibrate parallel to (back and forth along) the direction the wave travels, creating compressions and rarefactions.