# The travelling wave: An intuition

The aim of this section is to understand the traveling wave solution.

We all know about our favorite function – ‘The sinusoid’.

$y$ becomes 0 whenever $sin(x) = 0$ i.e $x = n \pi (n=1,2,3 ...)$

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

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

As you can see this value of $x$ is dependent on the value of time $t$,which means that the points where $y=0$ moves to the right as time progresses.

$\text{(t=0)} x = n \pi$

$\text{(t=1)} x = n \pi + \omega$

$\text{(t=2)} x = n \pi + 2\omega$

Here is a slowly moving forward sine wave for reference.

You can now try to convince yourself that a sine wave moving to the left is given by :

$y= A sin(x + \omega t )$

** The general form of a traveling wave is $y = sin(kx - \omega t)$. For the sake of simplicity we have considered the case where $k=1$ but understand that you can apply the same argument to any value of $k$ as well.