class22lecnotes

class22lecnotes - Class 22 Wednesday March 3 2010...

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Class 22, Wednesday, March 3, 2010 Reading: /, 'rl2 I rf3 f /~, J Review from last class: fit t7 n c /1 A J 11::. I, 2, !. ... .' /) ~~ a.. 2) /.9re0oY/ p n :In c L·~ t7n. ./'t:/UbI.A If ~lMtt1I (M(p. ?I'YJKtIH~;'n 'fY'1b.1 .' n A ~n. - - tt Vn =- n. 1:= /vjiJ;ttr i CttJyJ ~X/~: Acoustic Interferometers An acoustic interferometer is a device that splits an original sound wave into two parts, traveling on slightly different paths, and subsequently recombining these waves to produce interference in a receiver. The interference can be constructive or destructive, depending on the phase difference of the two split waves. Since the waves originate from the same source, they are identical, so ~%=O, and hence the phase difference is given by the path-length difference between the two waves. A sketch of an acoustical interferometer can be found on the next page. r; :- a+b . } ~~ rz. = Z L rtf' 7- b :::: > (p AtI/rv cl/f(..t . t4.llruch'vL : - 22.. I
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,----- (2..---- f L (v~n~) , l--~~ --"'" ~~--I._ ... __ ~_I. __ ~_ () - V"~ , {)i1t'C/Pr j(JUI..c.E: /4IIl"",F----- r, ~ __ .... I -I , \_ a ,.~ b ... f L /J:: 0, /, 2) ... Hence, if you change the length L of the U-shaped tube, you change the path-length difference between the two waves. You will record alternate minima and maxima according to the interference condition that is met for each specific length L. By counting the number of max-min-max cycles recorded in the receiver, you can infer the wavelength of sound. If the length of the U-tube was changed by an amount AL, and you count a number Am of max-min-max cycles, then: - I An=AL/()"/2). J Example ~ Assume that as you change L to L' your receiver makes the transition from a maximum of sound to a minimum. How much did the length L change? How much does it need to change in order to hear once again a maximum? .2L= n}, ) =) tJL .- ¥ t (-lMI) ~I = ,2L'::: (211-1/)A 2 =}f~ff=f . f-o I 'k; fro U-l () U( 1M PI X. IP .a /kl '( f tu/{,.-f. r t" c,u i-(,o p c;t,. ~ g CIA L 1-f. I .lL=n;\ ) '=> IoL= ~-I:! /) -r- =y4f-~ .2 L '= ( /)-1/ ) /\ :1 z. /hi Y t' Pua x /t)tWIt:/:! d ~AM' ~ ~ 2Z.2
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Optical Interferometers: The Michelson Interferometer I I I , ( JCY(W j ___ ~ ___ 41" ~ ~ jfilrror Z r z. This instrument is used, for example, to make accurate measurements of the wavelength of visible light or to determine indices of refraction. Here the beam gets split by a beam splitter, a partially silvered mirror, which reflects one half of the incoming light and transmits the other half. The mirror M2 can be moved back and forth, which changes the path-length of the second wave, hence changing the path-length difference Ar. Since the two beams are derived from the same source, they have identical initial phase Aq>o. Hence the total phase difference between these two beams is given only by the path-length difference, and the condition for destructive and constructive interference is set up with respect to this path-length difference. This is recorded as a bright central fringe in the detector, if the interference is constructive and as a dark central fringe if it is destructive.
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