The wave equation says speed = frequency × wavelength, or v = f × λ. It links three quantities you can measure in a ripple tank, on a rope or from a diagram, and it appears in almost every wave question.
This lesson sits inside wave behaviour. It builds on the unit habits from measurement and quantities.
What do the three quantities actually mean?
The wavelength λ is the distance from one point on a wave to the same point on the next wave, such as crest to crest. It is measured in metres.
The frequency f is the number of complete waves passing a point each second. One wave per second is 1 hertz (Hz). The speed v is how far the wave pattern moves each second, in metres per second (m/s).
If f waves pass each second and each is λ long, the pattern advances f × λ metres every second. That is the whole reason the equation works.
How do I use it without slipping?
- Write the quantities you are given with their units, and mark which one is asked for.
- Convert to base units: hertz, metres, seconds. So kHz becomes Hz (× 1000), cm becomes m (÷ 100), and a period becomes a frequency by f = 1 ÷ T.
- Rearrange first: f = v ÷ λ and λ = v ÷ f.
- Substitute and calculate, then state the unit.
- Check the size: a ripple on a tank moving at 300 m/s would be a warning sign.
Worked example
A dipper in a ripple tank makes 12 waves in 3.0 s. A student measures the distance across 5 complete waves as 0.30 m. (Invented example data.) Find the speed of the waves.
Step 1, frequency: 12 waves in 3.0 s gives f = 12 ÷ 3.0 = 4.0 Hz.
Step 2, wavelength: 5 waves span 0.30 m, so one wavelength is 0.30 ÷ 5 = 0.060 m.
Step 3, equation: v = f × λ = 4.0 × 0.060 = 0.24 m/s.
Step 4, check: v ÷ f = 0.24 ÷ 4.0 = 0.060 m, which matches the wavelength. A speed of 0.24 m/s is sensible for shallow-water ripples.
The mistake to watch for
A frequent slip is to use the length of the whole measured stretch as the wavelength.
Mistaken answer: v = 4.0 × 0.30 = 1.2 m/s
The 0.30 m covers five waves, not one, so the speed is five times too large.
The correction is to ask, every time, “how many wavelengths does this distance contain?” and divide by that number. The same care applies to units: a wavelength read as 6.0 cm must become 0.060 m before you multiply.
The bounds and rounding explainer is useful when a measured wavelength has only two significant figures and you want to see how that limits the speed.
Check yourself
1. A sound of frequency 50 Hz has wavelength 6.8 m. Find its speed.
Show answer
v = f × λ = 50 × 6.8 = 340 m/s.
2. A radio wave travels at 3.0 × 10⁸ m/s and has frequency 1.5 × 10⁸ Hz. Find its wavelength.
Show answer
λ = v ÷ f = (3.0 × 10⁸) ÷ (1.5 × 10⁸) = 2.0 m.
3. A wave on a rope has period 0.020 s and wavelength 0.50 m. Find its frequency and speed.
Show answer
f = 1 ÷ 0.020 = 50 Hz. v = 50 × 0.50 = 25 m/s.
Where this leads next
Next, look at what the height of a wave tells you in reading amplitude without doubling it. When you are ready, test the whole module with the wave behaviour practice set.
Some students follow each step here but still lose marks when the question hides the units or the count of waves. That is where our online one-to-one Physics tuition can help, because a teacher sees the working as it is written.