## Rolling Shutter and online guitar videos

When you search for videos online of plucking a string on an instrument such as the guitar, a surprising number of searches lead you to videos such as the following:

This is not how plucked strings look like! And they don’t have anything to do with Harmonics either! The reason why you are seeing those shapes on the guitar is due to the rolling shutter effect on your camera.

But if you do want to see how plucked strings look like, the following videos would be your best bet:

What is Rolling Shutter?

DIY: Tutorial running you through how you can recreate the effect on a guitar for yourself

## Even and Odd Harmonics of a vibrating string

In the previous section we took a look at the vibrating string fixed at both ends and found that in order for the boundary condition to be satisfied, the following are the only solutions possible:

The solutions on the left of the image are often termed as ‘Odd Harmonics’ because they have odd number of anti-nodes and the ones of the right have even number of anti-nodes hence ‘Even Harmonics’

If you pluck a string right at the center, you are essentially exciting only the odd harmonic components.

You can test this out by taking a string instrument and plucking it at the center. Download a spectrum app on your phone and take a look at the spectrum

You will see peaks in the spectrum only at the frequencies which correspond to the odd harmonics:

String instruments like the violin or guitar are plucked off-centered, so you get both the odd and even harmonics. But what differentiates one instrument from the other is the amplitude at which these harmonics are expressed when you play them.

Do watch the following video if you would like to know more:

## Standing Waves

If you have a solid understanding of what Traveling waves are (click here if you need a refresher) then when you add up a sine wave moving to the right with a wave moving to the left, you get a standing wave.

$y(x,t) = \sin(kx-\omega t) + \sin(kx + \omega t)$

Using $\sin(a) + \sin(b) = 2 \sin((a+b)/2) \cos((a-b)/2)$ and simplifying the above equation we get :

$y(x,t) = 2\sin(kx)\cos(\omega t)$

A plot of this looks like the following: Red circles denote the nodes where the amplitude of vibration is 0. Anti nodes on the other hand are the regions of maximum amplitude oscillations.

For the most part when one is referring to standing waves, it is customary to just talk about the resultant wave that you see above.

But one should understand that the way you form this is by taking a right moving wave and adding it up with a left-moving wave: