### Browsed byCategory: physics

Commutation relation in QM (using Index notation)

## Commutation relation in QM (using Index notation)

When I was learning about commutation relations in QM, this website served as a good resource. Inspired from that here’s a compiled list of commutation results which I found helpful and some notes on how to use index notation to see why that relation would be true. Link to pdf file

DIY Pilot wave hydrodynamics

## DIY Pilot wave hydrodynamics

Approximately two years ago, I wrote a series of posts covering Pilot wave hydrodynamics with Nicole Sharp from FYFD. Since then I have always wanted to try this out at home and visualize the phenomenon. Following is an informal report on how I was able to get this to work from things I found at home: Things needed A sub-woofer or a woofer Petri dish Dropper Cardboard Hot glue Vegetable/ Silicon/ Linseed oil Setup One of the first things that…

Using ray diagrams to better understand everyday reality – Demo

## Using ray diagrams to better understand everyday reality – Demo

One of the easiest way to visualize ray diagrams for lenses is by using an array of arrows on the board as the object and the camera on your phone as the screen. (i) Convex Lens : Arrows on the board are placed outside the focal length of the lens -> Inverted image (ii) Convex Lens :Arrows on the board are placed inside the focal length of the lens -> Magnified Erect image (iii) Concave Lens: Irrespective of whether you…

Physics of invisibility

## Physics of invisibility

(This page will be updated as the quarter progresses with other techniques that you will eventually learn about) There are many way to make things “disappear” and impart the illusion of invisibility. Based on what you have studied so far, here is one possible ways you can do so. (There are certainly other ways and I strongly recommend spending some time thinking about this) Using the refractive index If you want to make something invisible,you have to ensure that the…

Van Gogh’s The Starry Night, Turbulence and Adaptive optics

## Van Gogh’s The Starry Night, Turbulence and Adaptive optics

Van Gogh’s The Starry Night is a stunning painting that artistically brings out the effect of turbulence in our atmosphere. And this turbulence of air in addition to the effect of varying refractive index of the layers in our atmosphere causes the twinkling of stars: If you are an astronomer trying to study the cosmos from the earth, this turbulence of air and twinkling of stars is a total nightmare. The last thing that you want the light that painstakingly…

Rolling Shutter and online guitar videos

## 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…

Visualizing Doppler Effect using ripple tanks

## Visualizing Doppler Effect using ripple tanks

Ripple tanks are really cool ways to explore the way a wave behaves under the influence of a perturbation. They are fairly simple to make, and are usually available in college and school laboratories to render better understanding of the wave phenomenon. How does it work ?                    Source There is a usually an oscillating paddle( above– used to produce plane waves) or a point source/s ( below – used to produce circular waves ) which are actuated by eccentric…

Even and Odd Harmonics of a vibrating string

## 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…

Standing Waves

## 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…