In this activity, you will be introduced to the wave equation, which will allow you to calculate a speed, wavelength, or frequency of a wave.

**Frequency and wavelength**

All waves have a frequency and a wavelength. Frequency is the number of waves per second and is measured in Hertz (Hz), while wavelength is the distance between two peaks, measured in metres.

Now, imagine a wave that is travelling at a constant speed, such as a wave on an oscilloscope screen.

What would happen to the wavelength if the frequency increased? Let's take a look at the effect.

From left to right, the three different waves have been produced by **increasing the frequency.**

You will notice that the wavelength has decreased, and this makes sense. Producing more waves every second will 'squash' the wave into a smaller space, resulting in peaks that are closer together.

If we now examine closer and put some measurements into this, we will start to realise there is a mathematical relationship between frequency and wavelength:

In this case, **doubling the frequency halved the wavelength**.

Furthermore, we then multiplied the original frequency by 4 and the original wavelength divided by 4.

So if we multiply one quantity by a given value, the other quantity divides by that same value.

Also notice that multiplying the pairs of values together gives the same answer each time (2 x 12, 4 x 6, and 8 x 3 all make 24). This is called **inverse proportion**.

**The wave equation**

As we have just seen, frequency and wavelength are inversely proportional for a wave with a constant speed. The equation that relates these quantities is as follows:

**Speed (m/s) = Frequency (Hz) x Wavelength (m)**

In symbols, it is: **v = f λ**

where v = velocity (speed), f = frequency, and λ = wavelength. (λ is a letter of the Greek alphabet called 'lambda').

So, you can calculate the speed of a wave by multiplying the frequency and wavelength together.

The equation can also be rearranged to find frequency or wavelength:

**f = v ÷ λ
λ = v ÷ f**

So, as long as you use the equation in the correct arrangement, you will always be able to calculate a speed, wavelength, or frequency of a wave.

Just make sure that frequency is in Hertz and wavelength is in metres, otherwise your units will not produce a speed in metres per second.

Now that you have seen the equation, have a go at using it in the upcoming questions.