# How to visualise the motion of a wave moving on a string as observed by moving in the same direction and with the same velocity as the wave?

I am a High School student and was reading Wave Motion and Waves on a String from a popular Indian textbook of Physics, "Concepts of Physics" by Prof. HC Verma.

In the derivation of a wave velocity on a string,the author asks one to visualise the condition as follows:

"Suppose a wave y=f(t - x/v) is travelling on the string in the positive x-direction with a speed v. Let us chose an on observer who is riding on a car that moves along the x-direction with the same velocity v. Looking from this frame, the pattern of the string is at rest but the entire string is moving towards the negative x-direction with a speed v. If a crest is opposite to the observer st any instant,it will always remain opposite to him with the same shape while the string will pass through this crest in opposite direction like a snake. "

Tried to find animations which can help me with the visualisation by searching keywords but couldn't find any.

If anyone can post a relevant animation or simplify the extract for me and make it easier to understand,it would be of great help.

Sorry if this is an obvious or easy-to-understand extract. I am generally good at English,but I think failure to understand the extract para properly has somewhat to do with English not being my first language.

Thank you!!

If you are driving alongside a tight string that has no wave, you will see the straight string moving past you. Now if the same string has a wave in it, and you are driving alongside it at the same speed as the wave is moving down the string, you will still see the string moving past you, but you will no longer see it as straight. You will see it curved by the wave that you are moving alongside of.

• Thanks a lot man !!! Got it. :D – Yuvraj Singh Sep 9 '19 at 18:19

Instead of the string imagine that there is river and on the water there are some water waves which are moving relative to the shore.

Here is an animated gif of surfers riding a tidal bore with the water waves travelling from left to right.

You will see that the surfers do not move relative to the crest of the water wave just behind them, so they are moving at the speed of the water wave towards the right.

Now look carefully at the gif in the region enclosed by the red rectangle below with the surfer $$a$$ abd the shadow of a tree $$b$$.
The surfer is moving with the water wave and hence the shore and the shadow of the tree is not moving relative to the shore.

I have two stills of the enlarged the area enclosed by the red rectangle with the surfer moving from position $$a$$ to $$a'$$ relative to the shore whereas the shadow of the tree does nor move relative to the shore.

You now have to imagine what the surfer observers.

The surfer observers the shadow of the tree moving towards her, ie the shore / on the shore / the string are moving from right to left.

• Thanks man!!! Got it. :D – Yuvraj Singh Sep 9 '19 at 18:18