PHY 206 SPRING Problem #1 NAME: SIGNATURE: UM ID: Problem #2. Problem #3. Total. θ r =θ a. Prof. Massimiliano Galeazzi. Midterm #3 April 5, 2006

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1 PHY 06 SPING 006 Pr. assimilian Galeazzi idterm # Aril 5, 006 NAE: Prblem # SIGNAUE: U ID: Prblem # Prblem # tal Sme useul relatins: Wae equatin: Dler shit: Intensity: Fr eridic wae: I A w y( x, t) y( x, t) x t + L L S + S (remember sign cnentin) Pwer I Area max ρb ρb Seed ragatin sund in ideal gas: Light relectin: Light reractin: θ r θ a n sin θ n a a b sinθ b

2 Questin # Cnsider an rgan ie length L en at the let end and clsed at the right end.. D yu hae a dislacement nde r antinde at the let end the ie? At the right end?. Using the axes belw, draw the amlitude y the sund waes rduced in the ie as a unctin the distance x alng the ie r the irst three mdes the ie.. Frm yur drawings, derie exressins r the waelengths the irst three mdes the ie as a unctin the length L.. Frm yur answer t art, derie an exressin r the requency the irst three mdes (assume that the seed sund waes in air is ). 5. I the intensity the sund rm the ie at a distance d is 0 db (decibels), hw ar away rm the ie can yu hear its sund (remember that the threshld r human hearing is abut 0 db). 6. A secnd ie, identical t the irst ne, is layed at the same time as the irst ne. Hweer, the secnd ie is clder than the irst ne and the sunds rm the tw ies rduce a beat with beat requency. What is the dierence in temerature between the tw ies? Cnsider the air as an ideal gas. NOE: Yu may ind useul the exressin used in class, r a generic unctin y(x) and dy small changes in x: y x. dx n n n ) Let: ressure nde, dislacement antinde ight: dislacement nde, ressure antinde. ) n: L, L n: L, L 5 n: L, L 5 ), therere: n: L n: L n: 5 L 5) I β (0dB) lg, I β at d, I 0 I 0 db I 0, When β0, I I. But, r the inerse square law: I Id Id, d d d 0 I

3 6) i the ies are identical, the waelength des nt change, but the requency changes due t the dierent temerature the air. Als (slutin ): ( ) ( ) ( ) [ ] + at irst rder in :, which is the same result btained bere.

4 Questin # A hrizntal light beam is incident n a rism as in the igure. he angles A the rism are 5, the index reractin the rism is n, while the index reractin air is arximately.. Draw the light beam as it traels thrugh the rism.. Calculate the angle between the initial directin the light beam and its directin ater the irst reractin.. Calculate the angle between the initial directin the light beam and its directin ater the secnd reractin.. I the waelength the light in air is, what is its requency in air? 5. What are its requency and waelength inside the rism? 6. Nw assume that, instead, the beam is cmsed white light and that the index reractin the rism is deendent n the waelength. In articular, assume that the index reractin is greater r lnger. What haens t the beam ater the tw reractin? Exlain in n mre than a ew wrds. 7. Which clr the rainbw cmes ut the rism tward the sitie y directin and which ne cmes ut tward the negatie y directin?. sinθa sin A. sin θa nsinθb θ a 90 A 5 A θ b sin sin n n sin A δ θa θb A sin n. θ c 90 θb nsin θc sinθd sin A sin A sinθ d nsin( 90 θb ) nsin 90 sin ncs sin n n n δ θb A n sin sin A A sin sin n n n sin A n A

5 c. 5. he requency des nt change: n c, 6. he dierent clrs are reracted at dierent angles and yu see the rainbw 7. he angle δ is mntnic in n, and it increases i n increases, therere lnger waelengths will be reracted mre, and the red will be tward the negatie y directin, while the blue will be tward the sitie y directin.

6 Questin # A truck and a lice car are araching each ther with relatie seed. he siren the lice car is rducing a sund with requency.. Is this inrmatin suicient t determine the requency the sund heard by the drier the truck? Exlain in a ew wrds.. I the lice car is traeling at seed, what is the requency the sund heard by the drier the truck?. What is the requency the sund heard by the drier the truck when the tw ehicles hae assed each ther?. Nw suse the sund rduced by the lice car is relected rm a wall that is in rnt the car. he drier the lice car therere hears the beats rduced by the cmbinatin the direct siren sund and the sund relected rm the wall. What is the beat requency? 5. he drier the lice car decides t increase the lume the siren, s that the intensity the sund wae is dubled. What are the change in the amlitude and ressure amlitude the sund wae?. N, yu need t knw the indiidual seed with resect t the air.. Let s call the sund seed car + L car, + S using the rer sign cnentin: car + +. he cars are nw receding rm each ther, car +. wall + + wall I A, the amlitude is increase by I max, the ressure amlitude is als increase by

PROBLEM 1-10 points. [ ] n 1 >n 2 >n 3 [ ] n 1 >n 3 >n 2 [ ] n 2 >n 1 >n 3 [ X ] n 2 >n 3 >n 1 [ ] n 3 >n 1 >n 2 [ ] n 3 >n 2 >n 1

PROBLEM 1-10 points. [ ] n 1 >n 2 >n 3 [ ] n 1 >n 3 >n 2 [ ] n 2 >n 1 >n 3 [ X ] n 2 >n 3 >n 1 [ ] n 3 >n 1 >n 2 [ ] n 3 >n 2 >n 1 PROBLEM - 0 pints [5 pints] (a) Three media are placed n tp f ne anther. A ray f light starting in medium experiences ttal internal reflectin at the tp interface but sme f the light refracts int medium