Wave questions often give you an observation in words and expect a number back. The key is v = f × λ: wave speed equals frequency multiplied by wavelength. The skill is deciding which two quantities the observation gives you.
This lesson sits in integrated physical reasoning because it combines counting, measuring, unit conversion and a physical explanation in one answer.
How do I read a wave observation?
An observation usually hides one of three things: a count in a time (gives frequency), a distance covering several waves (gives wavelength), or a change of medium (tells you which quantity must stay fixed).
- Frequency: divide the number of complete waves by the time in seconds.
- Wavelength: divide the measured distance by the number of wavelengths it spans, then convert to metres.
- Speed: multiply frequency and wavelength.
- Change of medium: the source sets the frequency, so frequency stays constant and speed and wavelength change together.
- Unit check: wavelength in metres, frequency in hertz, speed in m/s.
Worked example (invented data)
In a ripple tank, a student counts 15 waves passing a marker in 10 s. Using a ruler on a photograph, she finds that 5 wavelengths cover 40 cm. The ripples then enter a shallower region where the wavelength shortens to 5.0 cm.
Find (a) the frequency, (b) the wave speed in the deep region, (c) the wave speed in the shallow region.
(a) Frequency. f = 15 ÷ 10 = 1.5 Hz.
(b) Deep region. One wavelength is 40 ÷ 5 = 8.0 cm = 0.080 m.
v = f × λ = 1.5 × 0.080 = 0.12 m/s.
(c) Shallow region. The source has not changed, so f is still 1.5 Hz. λ = 5.0 cm = 0.050 m.
v = 1.5 × 0.050 = 0.075 m/s.
Re-check: in centimetres, 1.5 × 8.0 = 12 cm/s = 0.12 m/s, and 1.5 × 5.0 = 7.5 cm/s = 0.075 m/s. The wave is slower in the shallow region and the wavelength shortened in the same ratio, 5.0 ÷ 8.0 = 0.625, and 0.075 ÷ 0.12 = 0.625.
The mistake to watch for
A student assumes the frequency changes when the wavelength changes, then uses the old speed.
Mistaken working: “The wavelength went from 8.0 cm to 5.0 cm, so the speed stays 0.12 m/s and the frequency must have risen.”
The source has not changed, so the frequency cannot change. The speed is the quantity that depends on the medium.
A second slip is mixing units: 1.5 × 8.0 = 12 is only 12 m/s if you forget that 8.0 is in centimetres. Convert before you multiply, or state the unit as cm/s.
Check yourself
All data are invented.
1. A sound wave of frequency 440 Hz travels at 330 m/s in air. Find its wavelength.
Show answer
λ = v ÷ f = 330 ÷ 440 = 0.75 m. Check: 440 × 0.75 = 330.
2. A radio wave has a frequency of 100 MHz (1.0 × 10⁸ Hz) and travels at 3.0 × 10⁸ m/s. What is its wavelength?
Show answer
λ = (3.0 × 10⁸) ÷ (1.0 × 10⁸) = 3.0 m.
3. Waves on a rope have a period of 0.25 s and a wavelength of 0.30 m. Find their speed.
Show answer
Frequency = 1 ÷ 0.25 = 4.0 Hz. Speed = 4.0 × 0.30 = 1.2 m/s.
Where this leads next
The same habit of naming what stays fixed helps in connecting thermal transfer with particle behaviour. If you want to see how an observation like this becomes a judged conclusion, try the scientific investigation critic, and test yourself in the integrated practice set.
Students who recall formulas but lose marks on explanations often need someone to read their sentences back to them. That is a natural focus in online one-to-one Co-ordinated Sciences tuition.