Drop a pebble in a pond and ripples spread out. Shake one end of a rope and a wiggle runs along it. A wave is a disturbance that travels, carrying energy from place to place. Four numbers describe a repeating wave, measured in SI units: meters, seconds and hertz.
Key idea
Amplitude: how far the medium moves from rest (rest to crest). Wavelength $\lambda$: the length of one wave, crest to crest. Frequency $f$: how many waves pass each second, in hertz (Hz). Period $T$: the time for one wave, so $$T = \dfrac{1}{f}$$
Why it works
If 4 waves pass every second, each one takes a quarter of a second: $T = \tfrac{1}{4} = 0.25$ s. Frequency counts waves per second; the period is seconds per wave, so each is 1 divided by the other. Bigger amplitude means more energy: a tall ocean swell hits the beach far harder than a ripple.
Worked example: Period from frequency
A buoy bobs up and down 5 times every second as waves pass. Find the frequency and the period.
- Frequency: 5 waves per second, $f = 5$ Hz.
- Period: $T = \dfrac{1}{5} = 0.2$ s for each wave.
Answer: $f = 5$ Hz, $T = 0.2$ s
Worked example: Wavelength from crests
A photo of a rope wave shows crests at 1.5 m, 4.5 m and 7.5 m along the rope. Find the wavelength.
- Wavelength is the distance from one crest to the next: $4.5 - 1.5 = 3$ m.
- Check with the next pair: $7.5 - 4.5 = 3$ m.
Answer: 3 m
Common mistake
Thinking a wave carries the water or the rope along with it. A duck on a pond bobs up and down as waves pass, but it doesn't ride away with them. The medium moves back and forth around one spot; only the energy and the wave shape travel.
Common mistake
Measuring amplitude from crest to trough. That distance is twice the amplitude: the amplitude is measured from the rest position.