6.1 Periodic Waves

What Makes a Wave Periodic

A periodic wave repeats a pattern of disturbance at regular time intervals, transferring energy without transferring matter. Key traits include amplitude (max displacement from equilibrium), wavelength (λ, distance between repeating points), period (T, time for one cycle), and frequency (f, cycles per second). Frequency and period are reciprocals: f = 1/T.

Wave Speed and the Wave Equation

A wave's speed v depends on the medium's properties, not on frequency or amplitude. The relationship v = fλ connects speed, frequency, and wavelength. If frequency increases while speed stays constant (same medium), wavelength must decrease proportionally — they are inversely related for fixed v.

Transverse vs. Longitudinal Waves

In transverse waves (e.g., light, waves on a string), particle motion is perpendicular to the direction of wave travel, creating crests and troughs. In longitudinal waves (e.g., sound), particle motion is parallel to wave travel, creating compressions and rarefactions. Both types carry energy through oscillations of the medium (or fields, for EM waves).

Key terms

Periodic wave

A wave that repeats a regular pattern of disturbance at fixed time intervals, transferring energy without transferring matter.

Wavelength (λ)

The distance between two consecutive identical points on a wave (e.g., crest to crest).

Wave equation

v = fλ — wave speed equals frequency times wavelength.

Transverse wave

A wave where particle motion is perpendicular to the direction of wave travel (e.g., light, waves on a string).

Longitudinal wave

A wave where particle motion is parallel to the direction of wave travel, creating compressions and rarefactions (e.g., sound).

Try an AP-style question

A sound wave has speed 340 m/s and frequency 170 Hz. What is its wavelength?

1. 57,800 m
2. 170 m
3. 0.5 m
4. 2.0 m