6b_samplefinal

6b_samplefinal - ' Problem #1 Shown below are five strings...

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Unformatted text preview: ' Problem #1 Shown below are five strings of identical mass density, each of which is tied to a wall at one end, while the other end passes over a frictionless pulley and supports a stack of weights. Bank the strings according to the frequency of their fundamental-mode standing waves, from highest frequency to lowest. (2* *’ ‘L "‘"fi HE intgledr [‘7 Pmblem ii I mm? {HM +rav€lfxfi 3‘11 0! meehuwx Vf‘FfaC'l‘Tve :ncIGK If). 5: (a; guffgkfg m fur—Faces O’F “Cm”: JFHIenwi- Objad‘y wH’ln anhmwm Timing; m, In}! H,” W (gnarl/1f- In eaoln coma] ‘I’L'c [WW 5+5ka ’he Surname. a+ 'J’Le game Mk of)- 45° ’5‘0 ‘J’La norma‘: - Pro)?\€w\ fl: 2 r x' 71,: [MAN 44%, 97947.9m mc 'emge; am; warren; skawn [palm {Tier Wf+m| (lo-H—ec( kw; 1mm}? 01C“L Ohc'me+er vaf‘ei’w'lg‘) Er eaok lens or MWWOW/ H9 qu?{ chi o Jed“ JE'I‘ancag €J<qw~2nfi "HA: [ry‘fl'f Pa‘L‘ks 5&0qu Mn JAM .4; «Cowl myth. xio ' x= I". 2,“ 2:, 4‘, am 6m 7m * I 1 t : I I i { Problem #3: True/False Mark each statement as true or false. If a statement isfalse, then correct it, by adding, deleting, or changing a few words, so that it becomes true. _ 1) If Alice is standing twice as far from a loudspeaker than in bob, then Alice will measure the sound waves to have twice the intensity (compared to Bob’s measurement). 2) If Alice is standing twice as far from a loudspeaker than in bob, then Alice will measure the sound waves to have twice the frequency (compared to Bob’s measurement). 3) Radio waves have a lower frequency than most other types of sound waves. 4) If earthquake waves pass from granite (where they travel quickly) into shale (where they travel more slowly), then their direction of travel might change. g) A wave will experience a half-cycle phase shift when it passes from a medium in which it moves quickly into a medium in which it moves slowly. 7} When sound passes from a medium in which it moves slowly into a medium in ' which it moves quickly, its frequency will not change. £4) A lens with a positive focal length "can only cast real images. Problem Sanity Check: _ As always on sanity check problems, do not set this problem up and solve it from scratch (unless you want to try for extra credit at the end.) Instead, think over the physical situation it describes, and examine the equations given as possible solutions. At most one of these solutions is correct; the others are fundamentally flawed or physically unreasonable. The problem: A rope of linear mass density m and length L hangs from the ceiling. The top end of the rope is fixed, and the bottom end is free. Someone plucks the lower end of the rope, creating a short transverse wave pulse of amplitude A which propagates upward to .the ceiling: /f/ ff/ What is the time I required for the wave pulse to reach the ceiling? The possible answers: ,4*_ __ 1—... flag? I‘M {Tlfa a) What should be the units on t? Which equati0n(s), if any, does this eliminate? b) By now, you know the drill on sanity checks: give me good reasons why each equation cannot be true, until at most one equation remains. Which one, if any, is left? c) You notice that none of the equations mention the string’s mass M. It seems that they should — after all, the wave speed depends on the string’s mass density. Explain briefly why in fact M cancels out, and doesn’t effect the final answer. Extra Credit: (Use the back of the facing page <——— as necessary.) Set up and solve this problem "for real" (as if we had given you the problem, but no proposed equations.) Note: To get the exact answer requires some calculus. But if you don’t feel like doing any calculus, you can get a good upper or lower bound to the answer by a simpler technique. If you do this —— and explain clearly whether your answer is an upper bound or a lower bound, and why — then you’ll still get quite a bit of extra credit. Problem #5 (20 points) An ambulance is driving east at a speed VA = 40 m/s. Ahead of it, a distancex= 800 m, a motorcycle also moves east at speed VC = 30 ms. The ambulance's siren emits sound at frequency f0 = 500 Hz. a) What frequency does the motorcyclist hear? A short time later, both vehicles are still moving the same velocity as before, but the ambulance is now only 400 m behind the motorcycle. b) Does the motorcyclist now hear a higher frequency than you calculated in part a, a lower frequency, or the same? Brieflyiustify your answer. The motorcycle pulls to the side of the road and is now at rest. The ambulance is still moving with its original velocity, and is now only 50 m behind the motorcycle. c) Does the motorcyclist now hear a higher frequency than you calculated in part a, a lower frequency, or the same? Brieflyjustify your answer. nab/em ii I4 ‘Hn‘m fiflw‘ 01C- an‘mwn mpmcfivg TIAng mg ,‘g meergeJ in o, [Fccufc‘ 0? TflCIPK W4 3 gown PTFOF €X€Pfiw~em+€ MJG know +kor} .l( we < R’s“; +Lfckhgg5’ m a 3 mm. H _ mm w 0‘09?er When at [agar wtwge WQV‘QIW'HW (In-vacuum) TS Aozéoonm rg (Inn/~11 (II—413 ‘F‘Jm/ “KL Obflrver M11733. reflec "F6! {99% T5 WV) veal? ale; ‘Huc‘l‘r‘ve. rm-l—ervfiermce. I I) On 4/11; clraymm above} 5%“ W +W‘0 TMFOF’I‘QN“ PorHA; [97 w\/\\\CL\ FC'Hec‘Leé Cm“ mach AH”: Gkgerv‘en C{EQ([7 innch an] POW!"— CA" w‘m‘oln «sf-"(ar- duper“ka Q P116195 SLFP+ (la/Q +6 WL‘20‘4‘TOW I ' are ’I’Le Pdgsiblo. Wavelemy—HAS (5%- .}/LL [var in w £11m :7. (YUL‘ may 93],,3 Marc flab“ OY‘L QW§V~W remeMLer work l i n8 4 L ‘5)! C) WW"? T9 Tie Hwy mFrqc—Hm 7,1 (19x m9 9? (1) W TL: OBQW‘WV rewlaces “J’La IQ9€r wf4’k one c990, JCLQWH¢ r wmlmwl omi nouv gee; Cowermcflt/c' TwirCr’perPnCQ UFFHL “Harch inflm‘. WW’V «‘5 “Ha lamfi‘ Facgibéz wawdé’vfifl‘ (“1 macaw) of fly; new Lager? CT+¢ Inch n€C€§$avliy MM Vmufl éfimum) Problem # 7: , Through a series of mishaps, I cat finds itself stranded on a strange planet. Fortunately, he retains his sense of priorities, and immediately sets out to find a patch of sunlight to sleep in. He finds a well-lit piece of ground with area A = 0.5 m2, and notes that when the sun is directly overhead, this area absorbs 0: 24000 J of energy over a time . intervai t=5 min. 2 S/ § Sam fifth} a) What is the intensity of sunlight striking this planet? After his nap, the cat makes some astronomical observations. This planet is located a distance b = 8.0x107 km from the center of its sun, and the sun itself has a radius a = 1.0)(106 km. b) What is the total power emitted by the sun? . Now while napping in the sunlight, the cat has a prophetic dream: he must find a _ way for a patch of ground to absorb Q = 2,400,000 Joules of heat in five minutes. ' (A hundred times what his original patch absorbed.) He has access to such simple cat tools as string, catnip, measuring tapes, and a spaceship capable of interplanetary travel. ‘ c) Describe (in reasonable quantitative detail) at least two ways that the cat could use the above tools to make his dream a reality: a patch of ground will absorb 2,400,000 Joules of sunlight in 5 minutes. Problem #8 (25 points) Two speakers are separated by a distance b = .2 m produce sound waves of identical frequencies. On the other side of a very large room — L = 50 m, which you can treat as much longer than the separation between the speakers — a person walks back and forth along the wall, measuring the intensity of the sound. She finds that when she stands on the center line as shown below, the sound waves interfere constructively. At a distance y: 12 m off the center line, she measures destructive interference for the first time. OWrLé’ncl- \lfew" R “r 1’0» 34 )1} k—— “Heir-*2 L“_ ‘—‘ ~—«—r w-——_7 {Mat grate"- )? b/ \j 72L) WELL égm‘efg Lit/Em _.,7 m. a) What is the frequency of these sound waves? (Assume the speed of sound - v: 340 m/s.) b) At what distance yfrom the center line will she again hear constructiVe interference? (There is more than one answer; you only need to give one.) The speakers are now adjusted so that they are out of phase at the source; speaker #2 lags 1/3 of a cycle behind speaker #1. c) When the experimenter stands on the center line (y: 0), does she now hear constructive interference, destructive, or neither? (:1) Find at least one point y where she will hear destructive interferenCe. [Metal-(L iambauj be. edm (yum ...
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This test prep was uploaded on 04/16/2008 for the course PHYS 6B taught by Professor Graham during the Winter '08 term at UCSC.

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6b_samplefinal - ' Problem #1 Shown below are five strings...

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