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class17lecnotes-1

class17lecnotes-1 - Class 17 Friday January 19,2010 Reading...

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Class 17, Friday, January 19,2010 Reading: Sections on ERes -+ f~ M .1M! ~ _ /3. ~. : rt = 1<)( - '-.J t .,.. <10 ~ ~:Ii'af /h".j:( - or ;;hpJf C;;H/JfM,.:;t . - /J:!!.fkJ? ~P- : /.J 9' = , (X.z. -XI) 7- 9b l -% I ~ .. _. j~ ftvr tJ/itJ;; tP' A ~ or ~ 1M'" ~ fiid/~ cJ ,- lAw, #/frtM ct taM t,t tIut "f? : I. J ~ X I a / wfw·ft Q ~ ;:: CJ 1 fo I :: ot. 1D'l- ~ 0 for ty~ . .' E\A\f'D ~x p .. C\ .. (\l[\ ~r( tJCf~ ff :- 71 lk W6Af{/j alit. (}f.$)/- I M Ih~. I~ tJI. =. Ali. .2 . [?> ~ ¢ (J I wi; & ~x =" j , y CPo :: 0 ~ 9bz.::;t fir tt~: 1 x tJ Cf = A~ ::-.(T .. ' . MIld ~fo F 0 l}Cfo .:.H _ 6'1.-/\ ---.J..-I-+4--/--J;-.~ 6~=fI ~ bX; ~ IJf :1J! )'.,.fi:::J17 /
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Next, we review the concept of constructive and destructive interference, which we introduced two classes ago. For example, what is the net result of overlapping the two waves represented in the figure below? These two waves are in phase. They will strengthen each other when they come together. We call it constructive interference. Waves that are in phase add up constructively. In the figure below there is an example of a perfect constructive interference. In this case, the amplitude of the resultant wave is twice that of the individual waves (which had equal amplitudes). 0) When two waves that are out of phase interfere, the outcome is a disaster. They weaken each other. We call this destructive interference. In the figure below you find two examples of destructive interference. In the first case, the waves obliterate each other. This is a perfect destructive interference. The amplitude of the resultant wave is zero. The second example represents two waves with slightly different amplitude, The amplitude of the wave that results from the superposition of these two individuals is a very low-amplitude wave. j,) ,"\ /-', rv \SiI\ \1)1)- \ ))) t 51 \. " I " .... \ ... ! ,"" r .:::' 0 fl'c(ljIqAen.. 1J,:: ~ r.flhtl}rrll~~~';iJ/ ... ~ :It x x x x {},Z
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0) , ; '~' x x
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Before we put these pieces together in a quantitative picture. we do an example. Example ~ft a) If you are standing in front of two side-by-side loudspeakers that play sound of the same frequency, and you hear no sound, what can you say about their phase difference? b) Speaker 2 is moved away from you until you hear maximum sound when the speakers are separated by O.75m.Thereafter, as the speaker is still moving, you hear that the sound starts to decrease again. What is the distance between the speakers when the sound intensity is again a minimum?
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