But how do we, sitting on earth know how rapidly a planet like Mercury which is around 48 million miles away is rotating ?
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).
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.
Whenever you see physicists talking about light, you might have noticed they prefer to use wavelength of the light rather than it’s frequency.
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:
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:
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!
On the other hand, here is how easy it is to measure the wavelength of the light:
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 : **
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:
In addition to this, you can also derive the energy of a photon using the relation:
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.
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
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 )
When the sources are not in perfect sync. ( there is a time delay between the two occurrences )
Pulse 1 : in phase , Pulse 2: out of phase ( Notice how the resultant pattern is a combination of the previous two patterns )
Pulse 1 and 2 – in phase ( Establishing Symmetry )
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.
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 )