# On the travelling wave: An intuition

The aim of this post is to understand the travelling wave solution. It is sometimes not explained in textbook as to why the solution “travels”.

We all know about our friend – ‘The sinusoid’.

$y = sin(x)$

y becomes 0 whenever sin(x) = 0 i.e $x = n \pi$

Now the form of the travelling sine wave is as follows:

$y= sin(x - \omega t)$

When does the value for y become 0 ? Well, it is when

$x - \omega t = n \pi$

$x = n \pi + \omega t$

As you can see this value of x is dependent on the value of time ‘t’, which means as time ticks, the value of x is pushed forward/backward by a $\omega$.

When the value of $\omega > 0$, the wave moves forward and when $\omega < 0$, the wave moves backward.

Here is a slowly moving forward sine wave.