wave physics

The simple harmonic oscillator

Anonymous asked: Please explain the intuition of solving the SHM equation.

Okay Anon! Here you go, this is my rendition.


The problem

You have a mass suspended on a spring. We want to know where the mass will be at any instant of time.

Describe the motion of the mass


The physical solution

Now before we get on to the math, let us first visualize the motion by attaching a spray paint bottle as the mass.

Oh, wait that seems like a function that we are familiar with - The sinusoid.

Without even having to write down a single equation, we have found out the solution to our problem. The motion that is traced  by the mass is a sinusoid.


But what do I mean by a sinusoid ?

If you took the plotted paper and tried to create that function with the help of sum of polynomials i.e x, x2, x3 … Now you this what it would like :

By taking an infinite of these polynomial sums you get the function Since this series of polynomial occurs a lot, its given the name - sine.

I hope this shed some light on the intuition of the SHM equation. Have fun!

How do we know light is a wave?

Before I answer this question, I’ll need to briefly go over a wave property called superposition. Basically, superposition is the idea that two waves can be in the same position at the same time, and interfere with each other:

When the two waves add to each other and make a larger wave, we call this constructive interference. When the waves cancel each other out, we call this destructive interference. 

Now we’re going to move on to the Double Slit Experiment. Basically, you shine a beam of light at a piece of metal, cardboard, etc with two slits in it, with a surface behind it where you can see the light hit it. 

If light is a wave, what we’d expect to see would be an interference pattern created by the light from the first slit interfering with light from the second slit, which is exactly what we see. It’s a pattern of constructive interference (brighter regions) and destructive interference (darker regions), looking like this:

These images are helpful:

that is how we know light acts as a wave!!

Watch on the-earth-story.com

Have you ever paid attention to how easily waves can sort sediments on beaches? Look at that single layer of darker grains at almost a constant depth. Grain motion on a beach is a function of water depth - deeper water has more force and can move denser grains, as long as the grains don’t get below the level where waves move the water. Darker mineral grains are often denser than quartz, so the darker grains are gathering at a level where the ocean is able to move them around, while the less dense quartz grains are piled up above the the slightly shallower water.

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Ask Ethan: What Is Spacetime?

“Conceptually, the metric tensor defines how spacetime itself is curved. Its curvature is dependent on the matter, energy and stresses present within it; the contents of your Universe define its spacetime curvature. By the same token, how your Universe is curved tells you how the matter and energy is going to move through it. We like to think that an object in motion will continue in motion: Newton’s first law. We conceptualize that as a straight line, but what curved space tells us is that instead an object in motion continuing in motion follows a geodesic, which is a particularly-curved line that corresponds to unaccelerated motion. Ironically, it’s a geodesic, not necessarily a straight line, that is the shortest distance between two points. This shows up even on cosmic scales, where the curved spacetime due to the presence of extraordinary masses can curve the background light from behind it, sometimes into multiple images.”

Sure, you know what space and time are. If you heard of Einstein and relativity, you might know that they’re not absolute quantities, but that how you experience distances and the ticking of clocks is dependent on your motion through the Universe. But did you also know that the addition of masses and gravitation to the theory didn’t just result in general relativity, but changed the way we viewed the Universe completely? If you told me the positions, momenta and all the other properties of all the matter and energy in the Universe, I could tell you everything thanks to general relativity. I could tell you what the Universe would look like and what its behavior would be at any point in time: past, present or future. I could tell you the birth and fate of the Universe, and I could do it with no uncertainty at all. General relativity might be incredibly complex, but it’s the most powerful classical theory of all.

Come get the incredible answer, complete with a description of the spacetime metric, to the simple question of what is spacetime on this week’s Ask Ethan!

Letters on Wave Mechanics. Schrödinger Planck • Einstein • Lorentz, Edited by K. Przibram for the Austrian Academy of Sciences, Translated and with an Introduction by Martin J. Klein, Philosophical Library, New York, 1967

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A 200 Year Old Lesson: Scientific Predictions Are Worthless Unless Tested

“So the next time you run across what appears to be a theoretical absurdity, either because you believe such a thing must be so or cannot be so, don’t forget the vital importance of putting it to the experimental test! It’s the only Universe we have, and no matter how solid the footing of our theoretical predictions, they must always be subject to the scrutiny of unrelenting and continuous tests. After all, you never know what secrets the Universe will reveal about itself until you look!”

For centuries, Newton’s theoretical predictions were as unassailable as physics got. His ideas about mechanics, gravitation and optics passed test after test after test. Yet around the dawn of the 19th century, one class of observations appeared to run counter to his assertions: light appeared to exhibit a wave-like nature. The phenomena of diffraction and interference could not be well-explained by a corpuscular theory of light. Towering scientific figures such as Fresnel, Fraunhofer and Poisson calculated what they expected from a wave-like theory under various conditions, with Poisson getting the most absurd result. In theory, light that was shined around a spherical obstacle should produce a shadow… with a brilliant bright spot at the center. This was ruled a victory by Newton for all, proving the wave nature of light’s absurdity.

Fools! For you cannot simply claim an absurdity without doing the experiment to check! The results, the lessons, and the work of Francois Arago must never be forgotten.

nature.com
Mysterious cosmic radio blasts traced to surprising source
Repeating bursts come from a faint, distant dwarf galaxy.

Astronomers have pinpointed the location of an enigmatic celestial object that spits out brief, but powerful, blasts of radio waves. Surprisingly, the source of these intermittent signals lies not in a bright galaxy but in a small, dim one, some 2.5 billion light-years from Earth.

The discovery begins to lift the curtain on the mystery of fast radio bursts, which have puzzled astronomers since they first described the signals in 20071. This detection has really broken open the gates of a new realm of science and discovery,” says Sarah Burke-Spolaor, an astronomer at the National Radio Astronomy Observatory in Socorro, New Mexico, and West Virginia University in Morgantown. She spoke in Grapevine, Texas, at a meeting of the American Astronomical Society.

Fast radio bursts appear to come from beyond the Milky Way and crop up seemingly at random across the sky. Although they last just milliseconds, the radio blasts can emit as much power as 500 million Suns.

Continue Reading.

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LIGO BEGINS NEXT SEARCH FOR GRAVITATIONAL WAVES:
NSF DIRECTOR REFLECTS ON THE LASER INTERFEROMETER
GRAVITATIONAL-WAVE OBSERVATORY’S NEWEST QUEST

Statement from National Science Foundation Director France Córdova regarding news that, after a series of upgrades, researchers have reactivated the twin detectors of the Laser Interferometer Gravitational-Wave Observatory (LIGO), and resumed the search for ripples in the fabric of space and time known as gravitational waves:

“The last time scientists from the NSF-funded Laser Interferometer Gravitational-Wave Observatory (LIGO) searched for gravitational waves, they succeeded.

They detected gravitational waves from merging black holes 1.3 billion light-years away.

Researchers devoted more than 40 years to get to this point, and the National Science Foundation – I’m proud to say – was there all along the way, providing critical support to make this scientific achievement possible.

Today, that journey continues.

Already LIGO has exceeded our expectations, and, like most of the scientific world and beyond, I am excited to see what a more sensitive, upgraded LIGO will detect next.

“The significance of this expanding ‘window to the universe’ cannot be stressed enough, as it will illuminate the physics of merging black holes, neutron stars and other astronomical phenomena that cannot be reproduced in a laboratory setting.

The world waits with eager anticipation of what we will see and learn next, all because of the long-range vision and skills of hundreds of researchers around the world.”

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Has LIGO already discovered evidence for quantum gravity?

“According to Einstein, a black hole’s event horizon should have specific properties, determined by its mass, charge and angular momentum. In most ideas of what quantum gravity would look like, that event horizon would be no different. Some models, however, predict notably different event horizons, and it’s those departure models that offer a glimmer of hope for quantum gravity. If we see a difference from what Einstein’s theory predicts, perhaps we can uncover not only that gravity must be a quantum theory, but what properties quantum gravity actually has.”

In 2015, LIGO collected data from a total of three candidate gravitational wave events, all of which were announced and released in 2016. These events verified the great prediction of Einstein: that decaying orbits should emit gravitational radiation with specific magnitudes and frequencies that distort spacetime in a particular, measurable way. But some quantum gravitational ideas modify the event horizon and the space just outside of it, creating the possibility that merging black holes will exhibit “echoes” superimposed atop the Einsteinian signal. For the first time, a team of theorists dove into the LIGO data to test this, and may have just uncovered the first evidence for quantum gravity in our Universe.

With the next run of LIGO already underway, be prepared to find out that gravity may be inherently quantum after all!

youtube

This video is a superb explanation and AMAZING visual demonstration of gravitational waves. If you need help imagining or understanding gravity waves, this is a fantastic resource.

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