Amplitude and Period

Amplitude and period describe how large a wave oscillation is and how long each oscillation takes.

Definitions

Quantity	Definition	Unit
Amplitude ($A$)	The maximum displacement of a point on the wave from its rest (equilibrium) position	m
Period ($T$)	The time for one complete wave to pass a point	s

Relationship between frequency and period

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

If the period is 0.02 s, the frequency is:

$f = \frac{1}{0.02} = 50\text{ Hz}$

Reading from a displacement-time graph

On a displacement-time graph:

• The amplitude is the maximum displacement from the centre line (not from trough to crest).
• The period is the time for one complete cycle (one full wave pattern).

Reading from a displacement-distance graph

On a displacement-distance graph:

• The amplitude is the same (maximum displacement from the centre line).
• The wavelength is the distance for one complete cycle (crest to crest or trough to trough).

Worked example

A wave has a period of 0.004 s and a wavelength of 1.36 m. Calculate the wave speed.

Step 1: find frequency.

$f = \frac{1}{0.004} = 250\text{ Hz}$

Step 2: find speed.

$v = f\lambda = 250 \times 1.36 = 340\text{ m/s}$

Common errors and how to correct them

Measuring amplitude from crest to trough. This gives twice the amplitude. Amplitude is measured from the rest position to the crest (or to the trough), not the full height.

Confusing period and wavelength. Period is a time (seconds); wavelength is a distance (metres). They describe different things, even though both relate to “one complete cycle.”

How to apply this in an exam

Read graphs carefully. Identify the axes first (time or distance). Measure period from the time axis and wavelength from the distance axis. Always measure from the same point on consecutive waves.