I came to know that people couldn't get much out of my last post about 'Anti-reflectivity,' simply 'coz they didn't know about the co-efficients of reflectivity and transmissivity. So here it is.
Consider a transverse "sinusoidal" wave travelling from a thin string to a thick one, across a 'joint'. Part of the wave is transmitted across the joint to the heavier string, part of it is reflected back to the thin one. Let the amplitude of the incident wave be Ai, and those of the reflected and transmitted waves be Ar and At respectively.
If the wave travels in the first string with a velocity v1, and in the second with velocity v2, give me the coefficient of reflectivity, i.e. Ar/Ai, and the coefficient of transmissivity, At/Ai.
P.S.: The reflected and transmitted waves could also undergo a phase change, which is depicted mathematically by r or t being negative.
Hint: Use the fact that the "joint" exists. That is to say that the two ends cannot be at two different points. Also use the fact, that an 'acute' bend in a stretched string can only be accounted for by infinite tension!
By the way, the tension in both strings is the same.. isn't it?
P.P.S.: Though conservation of energy is a consequence, if you're struck, you may want to use it. (:
If the wave travels in the first string with a velocity v1, and in the second with velocity v2, give me the coefficient of reflectivity, i.e. Ar/Ai, and the coefficient of transmissivity, At/Ai.
P.S.: The reflected and transmitted waves could also undergo a phase change, which is depicted mathematically by r or t being negative.
Hint: Use the fact that the "joint" exists. That is to say that the two ends cannot be at two different points. Also use the fact, that an 'acute' bend in a stretched string can only be accounted for by infinite tension!
By the way, the tension in both strings is the same.. isn't it?
P.P.S.: Though conservation of energy is a consequence, if you're struck, you may want to use it. (:
Not sure but i think
ReplyDeleteAr/Ai=(v2-v1)/(v1+v2)
At/Ai=2v2/(v1+v2)
Bhaiya please confirm the answer!
i think we'll wait till tomorrow for some more response.. (:
ReplyDeletewe were told to directly remember the resutls of reflected and refracted wave amplitudes ...
ReplyDelete@Vipul: you are right.
ReplyDeletewould you mind explaining the others how you did it?
@shivanker i too exactly don't know the exact derivation but i remembered this result!
ReplyDeleteCan you tell how is it derived?
But i can share a link from where i got what exactly happens and why?-:
The link is-:
http://www.physicsclassroom.com/class/waves/u10l3a.cfm
well.. this post was all about deriving it yourself..
ReplyDeleteok so here's what you need to do..
1.
position of the joint end of the first string = position of the joint end of the second string at all times
2.
slope of first string at the joint = slope of second string at the joint at all times
confirm by commenting if u tried and got/didn't get the correct result..
^ do read the last line of my previous comment..
ReplyDeletei see my post had a few errors.. the tension was to be assumed the same in both strings.. the joint was assumed of zero length, and hence massless, thus implying equal tensions in both strings, and again to make net force on it zero, the strings had to have equal slope at the joint..
ReplyDeletelet equation of the incident wave be yi(x,t), reflected be yr(x,t) and transmitted be yt(x,t)
and let x=0 at the joint
so the 2 equations would be:
yi(0,t)+yr(0,t) = yt(0,t)
{dyi/dx at x=0} + {dyr/dx at x=0} = {dyt/dx at x=0}
now the results, can be applied to light waves as well using n ∝ 1/v, and this is what was used in the anti-reflectivity post..
ReplyDelete@Shivanker
ReplyDeleteSorry i will definitely keep in mind the last point