The wave speed equation: wave speed as frequency times wavelength, the distance-over-time form, and rearranging to find frequency or wavelength.

What this dot point is asking

Edexcel statement 4.6 wants you to recall and use both forms of the wave speed equation: wave speed as frequency times wavelength, and wave speed as distance over time. You must be able to rearrange the equation to find any of the quantities.

The frequency-wavelength form

This is the form you reach for when a question gives frequency and wavelength. It says that the speed of a wave is how many waves pass per second multiplied by the length of each wave. Because it has three quantities, it rearranges two ways: $f = \dfrac{v}{\lambda}$ to find frequency and $\lambda = \dfrac{v}{f}$ to find wavelength.

The distance-time form

This second form is the ordinary speed equation applied to a wave, and is useful when you are told how far a wave travels in a given time (for example a sound echo or a ripple crossing a tank). Both forms give the same wave speed, so you can combine them: if you find the speed from $v = \dfrac{x}{t}$, you can then use $v = f\lambda$ to find a frequency or wavelength.

Units and a key fact

For electromagnetic waves, the constant speed in a vacuum links frequency and wavelength inversely: as one goes up, the other goes down. This is why gamma rays (high frequency) have very short wavelengths while radio waves (low frequency) have long wavelengths, a point that returns in the electromagnetic spectrum.

How Edexcel examines this

The wave speed equation is one of the most frequently examined calculations in the whole specification and appears on both tiers, both as a standalone problem and embedded in questions on the electromagnetic spectrum, sound and the core practical. The mark scheme usually awards a mark for the correct equation, so write $v = f\lambda$ (or $v = \frac{x}{t}$) before substituting, then a mark for substitution and a mark for the answer with its unit. Questions are set in all three rearrangements, so practise finding speed, frequency and wavelength. A favourite is to combine the two forms: measure a wave's speed from a distance and time, then use $v = f\lambda$ to find its wavelength or frequency. Unit conversions catch many candidates, so convert wavelengths to metres and check that frequencies are in hertz. For electromagnetic waves, examiners may give the speed of light and ask for a wavelength or frequency, testing standard form; here the inverse relationship between frequency and wavelength at fixed speed is the key idea.

Try this

Q1. A wave has a frequency of $50\,\text{Hz}$ and a wavelength of $2\,\text{m}$. Calculate its speed. [2 marks]

• Cue. $v = f\lambda = 50 \times 2 = 100\,\text{m/s}$.

Q2. A wave travels at $12\,\text{m/s}$ with a wavelength of $3\,\text{m}$. Calculate its frequency. [2 marks]

• Cue. $f = \dfrac{v}{\lambda} = \dfrac{12}{3} = 4\,\text{Hz}$.