The Wave Speed Equation

Use frequency, wavelength and wave speed to describe waves and solve calculations.

About 3 min read
  • Define wavelength, frequency and period
  • Use the equation v = fλ
  • Calculate wave speed from measurements
Before you start

You know that waves transfer energy without transferring matter, and that speed equals distance divided by time.

Describing a wave

A wave has a repeating shape. The distance from one point on a wave to the same point on the next wave is called the wavelength. The number of waves passing a point each second is the frequency. If you count more waves each second, the frequency is higher.

Definition: wavelength

The distance between one point on a wave and the same point on the next wave, measured in metres.

Definition: frequency

The number of waves passing a point each second, measured in hertz (Hz).

The wave equation

One wave moves forward by one wavelength in one period. If f waves pass each second, the wave travels f wavelengths each second. This gives the wave equation.

Wave speed

v = f × λ

Here v is wave speed in m/s, f is frequency in Hz and λ is wavelength in m. The period is the time for one wave, so T = 1 ÷ f.

Sound in air

A sound wave has frequency 170 Hz and wavelength 2 m. Find its speed.

Maths
v = fλ
v = 170 × 2
v = 340 m/s

Answer: 340 m/s

Convert first

Convert kHz to Hz and cm to m before you use the equation. For example, 3 kHz is 3000 Hz.

Exam focus
Say it like this“v = fλ = 500 × 0.6 = 300 m/s”
Not like this“500 × 60 = 30000” — The 60 cm wavelength must be converted to 0.6 m.
Common mistakeUsing centimetres or kilohertz in the equation without converting the units.

Practice

A wave has frequency 5 Hz and wavelength 3 m. Find its speed.
v = 5 × 3 = 15 m/s.
A wave has speed 20 m/s and wavelength 4 m. Find the frequency.
f = v ÷ λ = 20 ÷ 4 = 5 Hz.
Find the period of a wave with frequency 50 Hz.
T = 1 ÷ 50 = 0.02 s.
Going further
Radio waves travel at 3.0 × 10⁸ m/s. Find the wavelength of a 100 MHz signal.
100 MHz = 1.0 × 10⁸ Hz. λ = v ÷ f = 3.0 × 10⁸ ÷ 1.0 × 10⁸ = 3 m.

Quick check

Wave equation quick check

What is the unit of frequency?

Frequency counts waves per second, and one per second has this unit.

If wave speed stays fixed and frequency doubles, what happens to wavelength?

In v = fλ, frequency and wavelength must multiply to the same fixed value.

A wave has f = 4 Hz and λ = 0.5 m. What is v?

Multiply frequency by wavelength using the wave equation: 4 × 0.5.
Key takeaways
  • Wavelength is the length of one complete wave.
  • Frequency is the number of waves each second.
  • Wave speed = frequency × wavelength.
  • Convert to hertz and metres first.
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