Describing waves
Every wave, whether it’s sound, light or a ripple on water, can be described using a few properties. These help scientists compare waves and predict how they’ll behave.
The main properties
| Property | Symbol | Unit | What it tells us |
|---|---|---|---|
| Wavelength | λ (lambda) | metres (m) | How long each wave is |
| Amplitude | A | metres (m) | How much energy the wave carries |
| Frequency | f | hertz (Hz) | How many waves pass each second |
| Period | T | seconds (s) | How long one wave takes to pass |
| Wave speed | v | metres per second (m/s) | How fast the wave travels |
Wavelength
Wavelength is the distance from one point on a wave to the same point on the next wave, such as crest to crest or trough to trough. For longitudinal waves, it’s the distance from one compression to the next.
| Wave | Typical wavelength |
|---|---|
| Ocean swells | 50–300 m |
| Middle C on a piano (sound in air) | About 1.3 m |
| FM radio | About 3 m |
| Microwave oven | About 12 cm |
| Visible light | 400–700 nanometres (millionths of a mm) |
| X-rays | Smaller than an atom |
Amplitude
Amplitude is how far the medium moves from its rest position. It’s related to the energy a wave carries.
- Bigger amplitude sound waves are louder.
- Bigger amplitude light waves are brighter.
- Bigger amplitude ocean waves are taller and more powerful.
The energy of a wave is proportional to the square of its amplitude. Double the amplitude and the energy is four times greater.
Frequency
Frequency is how many complete waves pass a point each second. One hertz (Hz) means one wave per second.
| Wave | Frequency |
|---|---|
| Ocean waves | About 0.1 Hz |
| Lowest note humans hear | 20 Hz |
| Middle C | 262 Hz |
| Highest note humans hear | 20 000 Hz (20 kHz) |
| FM radio | 88–108 million Hz (MHz) |
| Wi-Fi | 2.4 or 5 billion Hz (GHz) |
- For sound, higher frequency = higher pitch.
- For light, frequency determines colour: red light has the lowest frequency we can see; violet has the highest.
Period
Period is the time for one complete wave to pass. It’s the opposite of frequency:
T = 1 ÷ f and f = 1 ÷ T
If 4 waves pass each second (4 Hz), each wave takes 1/4 = 0.25 s.
Wave speed
v = f × λ
The speed of a wave depends on the medium, not on frequency or amplitude.
| Wave | Medium | Speed |
|---|---|---|
| Sound | Air (20 °C) | 343 m/s |
| Sound | Water | About 1480 m/s |
| Sound | Steel | About 5900 m/s |
| Light | Vacuum | 300 000 000 m/s |
| Light | Water | About 225 000 000 m/s |
The trade-off
In the same medium, the speed is fixed. So if frequency goes up, wavelength must go down.
- A high-pitched whistle (high frequency) has short sound waves.
- A deep tuba note (low frequency) has long sound waves.
Examples
-
A sound wave in air has a frequency of 686 Hz. What’s its wavelength?
λ = v ÷ f = 343 ÷ 686 = 0.5 m -
A wave on a rope has a wavelength of 2 m and a frequency of 3 Hz. What’s its speed?
v = 3 × 2 = 6 m/s
Putting it together
| If you… | Wavelength | Frequency | Amplitude |
|---|---|---|---|
| Shake a rope faster | Shorter | Higher | Same |
| Shake a rope harder (bigger swings) | Same | Same | Bigger |
| Play a higher note | Shorter | Higher | Same |
| Play louder | Same | Same | Bigger |
Common mistakes
- Thinking louder sounds travel faster. Speed depends on the medium.
- Mixing up frequency and period. They’re opposites (reciprocals).
- Measuring amplitude from crest to trough. It’s measured from the rest line to the crest.
Try it yourself
- Draw a wave with a wavelength of 4 cm and an amplitude of 1 cm. Label the crest, trough, wavelength and amplitude.
- A pendulum swings back and forth once every 2 seconds. What is its period and frequency?
- A radio station broadcasts at 100 MHz. Radio waves travel at 300 000 000 m/s. What is the wavelength?
(Answers to 2 and 3: period 2 s, frequency 0.5 Hz; 3 m)
Quick recap
- Wavelength is the distance between matching points on neighbouring waves.
- Amplitude relates to energy, loudness or brightness.
- Frequency is waves per second (Hz); period is the time for one wave.
- Wave speed = frequency × wavelength.
- In one medium, higher frequency means shorter wavelength.