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’.

image

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:

image

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

image
image

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

image

Here is a slowly moving forward sine wave for reference.

image

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.

One thought on “The travelling wave: An intuition

  1. Pingback: Standing Waves - Cosmic NoonCosmic Noon

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