How do we know how fast planets are rotating?

Planets revolve around their axis.

But how do we, sitting on earth know how rapidly a planet like Mercury which is around 48 million miles away is rotating ?

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Doppler effect

This is a very interesting example of Doppler effect.

Radio waves are shot from the earth towards the surface of mercury, one side of the planet will be red shifted (since it is moving away from you) and the other will be blue shifted (since it is moving towards you).

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By measuring this apparent change in frequency, we can find out how rapidly mercury is rotating.

Using this method we have found out that the rotation period of mercury is approximately 58.6 days.

Thanks for asking rj1124a@a! Great question!

Related interesting topics:

* Radar detector as fast as possible

** Radars on Airplane – NASA

*** Fundamentals principle of Radar (1946 film)

Why is wavelength important than frequency ?

Whenever you see physicists talking about light, you might have noticed they prefer to use wavelength of the light rather than it’s frequency.

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This is not a slip of the tongue and there is a very simple reason to it.

It is convenient to measure the wavelength of light experimentally rather than its frequency.

Take the violet light of wavelength 400nm. If we calculate it’s frequency, it turns out to be:

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Why is this a problem?

Can’t we measure 7.5 x 10^14 Hz directly ?* There is a theorem by Nyquist in signal processing which states that:

The
minimum rate at which a signal can be sampled without introducing
errors, is twice the highest frequency present in the signal.

This means that if you want to measure the frequency of light accurately then you need to be sampling at 2*(7.5 x 10^14) Hz in order to measure it and this is incredibly hard to achieve this instrumentally!

Diffraction Grating

On the other hand, here is how easy it is to measure the wavelength of the light:

Take the source of light and pass it through a diffraction grating.

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Measure the angle(theta) between the highest intensity (zero order) and say the ‘nth’ order. (see diagram above).

Use the following formula for the wavelength : **

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where, d –  distance between the slits (will be provided by manufacturer of diffraction slit), n – order of the slit, theta- from measurement.

And voila, you have the wavelength of the light. That’s how simple it is to get the wavelength of a source light. Since speed of light is a constant, the frequency of light is found out from the following relation:

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In addition to this, you can also derive the energy of a photon using the relation:

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And so on and so forth. All of these following from a simple diffraction experiment! That’s why calculating the wavelength of light is so crucial.

Have a good one!


* There are some indirect means to do this. Check this physicsforum page for more.

** How do diffraction gratings work ?

Alternating wave pattern on Ropes

I saw someone working out with Battle Ropes the other day and this wonderful pattern emerged was absolutely fascinating. Of course, the waveforms are not purely sinusoidal but it helps us to understand why you see such patterns

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

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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.

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

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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 :

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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.

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

On the travelling wave: An intuition

The aim of this post is to understand the traveling wave solution.
It is sometimes not explained in textbook as to why the solution
“travels”.

We all know about our friend – ‘The sinusoid’.

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y becomes 0 whenever sin(x) = 0 i.e x = n π

Now the form of the traveling sine wave is as follows:

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

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As you can see this value of x is dependent on the value of time ‘t’,
which means as time ticks, the value of x is pushed forward/backward based on the value of  ω  .

When the value of ω > 0, the wave moves forward and when ω < 0 , the wave moves backward.

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Here is a slowly moving forward sine wave for reference.

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Have a great day!

On the travelling wave: An intuition

The aim of this post is to understand the travelling wave solution. It is sometimes not explained in textbook as to why the solution “travels”.

We all know about our friend – ‘The sinusoid’.

y = sin(x)

y becomes 0 whenever sin(x) = 0 i.e x = n \pi

Now the form of the travelling sine wave is as follows:

y= sin(x - \omega t)

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

x - \omega t = n \pi

x = n \pi + \omega t

As you can see this value of x is dependent on the value of time ‘t’, which means as time ticks, the value of x is pushed forward/backward by a \omega .

drawing

When the value of \omega > 0 , the wave moves forward and when \omega < 0 , the wave moves backward.

Here is a slowly moving forward sine wave.

nxg3p

A portal to another universe ?

That my dear friends is a CT scan machine. Stripped off all the body parts, you can see clearly see what goes on inside.

A computerized tomography (CT) or computerized axial tomography
(CAT) scan combines data from several X-rays to produce a detailed image
of structures inside the body.

                                            CT scan of Brain

Pretty cool, don’t you think ?

Extras

Difference between MRI and CT scan

Why dont you spin the patient instead ? – Awesome reddit thread

Better quality gifs : here

Source Video: Micheal Jonnson

Interference : An intuitive approach

Ripple tank experiments are probably one of the best ways to understand wave phenomenon. In this post lets explore the Interference phenomenon that leads to the distinct patterns formed in the Double Slit experiment.


When the two sources are in perfect sync ( there is no time delay between the two occurrences )

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When the sources are not in perfect sync. ( there is a time delay between the two occurrences )

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Pulse 1 : in phase , Pulse 2: out of phase  ( Notice how the resultant pattern is a combination of the previous two patterns )

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Pulse 1 and 2 – in phase ( Establishing Symmetry )

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Continuous Excitation

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Pretty cool eh ?

I hope this post provided you with the intuition on how these interference patterns are formed.

The same analogy can be extended for higher/lower wavelengths as well.

Have a great day!

* Source : Educational Services Inc-1964  and Aerodynamic generation of sound

** Previous post : Ripple tank experiments

EDIT

*** Play with Ripple Tanks – http://www.falstad.com/ripple/ ( Thank you @americanbrightside )

The holy grail of Electromagnetic Radiation

James Clark Maxwell’s theory of electromagnetism was published in 1865.

And one of the most crucial prediction that was made is that so called Electromagnetic waves existed and they moved at the speed of light ( and light was one such wave ).

Experimentalists around the world got to work to seek these waves and Heinrich Hertz was one of the first ones to verify maxwell’s predictions.

The discovery of EMW

The setup that Hertz used is shown below.

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                         Original source of image : DMGualtieri

Transmitter

The crux of transmitter setup is the spark gap. Think of this as the spark plug that is used in your vehicles and how the electrons jump across the air gap due to the high electric field

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                                                Source

Now, by using Capacitors and Inductors Hertz was able to alter the frequency of oscillation of this spark between the gap. These are known as L-C oscillations. ( Click here to know more on how they work )

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                                                  Source

Receiver

He just used a copper wire and bent it into a circle and placed 2 small brass spheres at each end.

Goddamn it, What happened ?                                         

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                                     Source: The secret life of machines

According to Maxwell’s theory, if electromagnetic
waves
were spreading from the oscillator sparks, they would induce a current
in the loop that would send sparks across the gap.

This was exactly what occurred when
Hertz
turned on the oscillator, producing the first transmission and
reception
of electromagnetic waves

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.

‘Sparked’ an innovation frenzy

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In this experiment Hertz confirmed Maxwell’s theories about the existence of electromagnetic radiation and also inadvertently inspired the invention of the Wireless Telegraph, Radio, TV and others.  

For this remarkable contribution, the SI unit of frequency has been named ‘Hertz’ in his honor.

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Thus, Physicists at the end of the 1900s had a new toy to play around with – Electromagnetic Waves !

Have a great day!