Understanding and applying the wave speed equation.

Waves transfer energy not material. They do this by making a medium oscillate. This oscillation, which is just a way of saying a repeated vibration, is passed along from one part of the medium, for example a substance like water, to the next. Lets return to our analogy of the waves crashing onto a beach. Imagine some inflatables bobbing up and down in the surf. They would not move towards the beach, they just oscillate up and down on the spot, just as the water they’re floating on does.

But the wave itself does move towards the beach!

We can therefore measure the speed of the wave. We can do this in the same way as measuring the speed of anything, just with measuring distance and time. Or we can do this with the wavespeed equation. You’ll need to be able to use both methods in GCSE Physics.

We'll start with the first, and I'll describe one of my favourite wave experiments. You can use a tray, the plastic type that we use in schools, fill it with water one centimetre deep. Prop up one end on a block, when you pull the block out the end of the tray falls and you can see a wave move from one end to the other and reflect back. Time this wave and calculate its speed. Fill the tray to two centimetres deep and repeat. What do you notice? That wavespeed in water depends upon the depth of the water. Interesting right.

I also used the same method, but with a bit more complicated apparatus to get measure the speed of sound in this video.

To do this we need to measure the frequency of the wave and the wavelength. Don't worry too much about the apparatus, or the experiment, that'll come in A Level, but basically you'd get the frequency by looking at electron oscillations in an oscilloscope and the wavelength by setting up standing waves. Bit at GCSE you need to be familiar with the equation, which we handily call the "wave speed equation". Wave speed = frequency X wavelength.

Think about the definition of those two things quickly. Wavelength is the length of one full wave cycle and frequency is the inverse of the time one full cycle takes. So it stands to mathematical reason that distance multiplied by the inverse of time equals speed. Get that? Well there's an easier way to get it: wavelength is measured in metres and frequency had units per second, so meters times per second equals metres per second.

Now we have a really simple formula that relates these three quantities and we can calculate any one of we know the other two. It's a really useful equation for analysing waves!

© Kit Betts-Masters kit@gorillaphsyics.com