Thursday, October 21, 2010

Intuitive meaning of Wavelength , Frequency and Velocity Relation -- Jithendrian

This is the one i consider as my best !!
As everyone knows velocity of a wave is the product of frequency and wavelength. The derivation for this is simple and given in so many text books using wave number. But I am totally confused how it can be intuitively and physically imaginable.First of all how to relate wavelength and frequency !! After a long try I came up with some analogy which will help you in thorough understanding of wave equations.Below derivations and concepts are 100 % my own work .. I am not telling this to boast myself but to tell the originality. So please feel free to comment/give feedback

Let us consider A and B are the source and destination . A is a gun and B Is the target
Length of the bullet = l
Distance between the gun and the target is d
Number of bullets shoot on the target = n
t be the time taken for the first bullet to reach the target as well as the total time taken for shooting n bullets



Assume that the bullets are shot continuously , n bullets with length l

Now the distance d can be expressed as


Another way to express d
Let v be the velocity of the bullet
t be the time taken to reach the destination
then


Equating (1) and (2) we get



We know when a first bullet reaches the target at time t there are n bullets are shot , number of bullets shot per second (k) is



Now put the equation (5) in (4)



Now come back to our electromagnetic wave (assume waves are as packet moving in a single path and not as particles )

Wave is like a bullet
Number of bullets shot per second (k) is the number of oscillations/vibrations or repetition of the waves per second which is nothing but frequency (f)
The length of the bullet (l) is the length of the wave (lambda)
Velocity of the wave (c) is the velocity of the bullet (v) Gun (trigger) acts as antenna finally interchanging the above form to



Substituing every thing(7,8,9) in equation 6 we get


Which is the bread and butter equation for a wireless engineer!!!

P.S all equations and pictures are made by me without copying :) using pptx and converted to image. If anything is not clear please let me know

10 comments:

Karthik.R said...

I found it difficult to understand. So definitely it should be a good work ;)

Think I crossed the age and reached a stage where I can't read more than 10 lines of technical stuffs. Equations..... Mmmhmmm.

Anyways, I appreciate your efforts and expecting some good technical feedback unlike mine :)

Scientist Jithu! :)

kosmos said...

You are becoming an Einstein. I never understood him though.

In your case, everything seems fine, except the huge assumption that waves are particles!! You coaxed Newton and Huygens,both in that statement, and became a competitor of Einstein... good work! But Einstein will debate you and so will the physicists.

--kosmos

jithendrian said...

Thanks Karthik , Actually I started reading communication related stuff but since everywhere frequency is playing a vital role , so to visualize frequency and wavelength i made an attempt , whether it is correct or not now i gained confidence of visualizing and expressing abstract ideas !!! anyway i need support from u people always :)

Deepak ,
Thanks for the feedback about assumptions.I need to check.
Yes I have to dive in to the 'electromagnetic wave' concepts :)whic will be helpful bot for me as well for ABB :) Let us see

Raj said...

Good explanation.....elementary but effective :-)

jithendrian said...

One of my co-researchers mentioned waves move like compressed and rarefacted along the medium , so l + delx and l-delx , but average is l which is mentioned as bullet length. so it is not a problem , wave or particle , it holds good for all.

Sri Harsha said...

nee thirundave matiya....

kiranmy said...

well everything is clear except for one thing that is your

kiranmy said...

Very nicely put down.Well everything is clear except for the first equation "d = n * l",I am not clear on that part ,how is the distance equal to number of bullets multiplied by their length.
How does it matter if the bullet length is varied ?I guess the number of bullets fired and the velocity with which it goes will only matter.

jithendrian said...

Thanks kiranmy
you are right , distance does not matter but i used distance for deriving and it is only for intermediate steps .. As i mentioned bullets are shot continuously so let t be time taken to shoot n bullets and the same is the time taken for the first bullet to reach so d = n *l if l increases since d is constant so n will decreases. This says when the wavelength is increased frequency is getting reduced

jithendrian said...

sorry wavelength increases frequency decreases is the wrong statement
if the wavelength is more frequency is less
Moreover this is other wave of intuitive proof of the concept thats all .. we can not entirely relate this with emwaves because emwaves is very huge topic in communication , physics and rfengineering so Its just a sample