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t12306s00 - PHYSICS 2306 TEST#1 18 February 2000...

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Unformatted text preview: PHYSICS 2306 TEST #1 18 February 2000 16M01-03 (4:00 PM Sections) 3”x5” Note Card and Calculator Allowed Salt} £19223 (Name - Printed) (Student ID.) (Signed Pledge - See Below) I pledge that the answers submitted by me represent oniy my work. Further, I pledge to refrain from communicating any information about this test to anyone until after the results of this test are returned. Please fill in the three entries specified above. Please record your answers to each question in the space provided. No partial credit will be allocated if your work is not shown. Please present your results coherently, otherwise you may lose some partial credit that you would otherwise receive. Make sure you provide the dimensions for each numerical answer; and specify the vector direction if the quantity is a vector. For many of the questions covering electrostatics you are asked to provide expressions for force or electric field, both of which are vectors. Your answers should be expressed in terms of a number, ke=1l4itsm some power of Q or IR, some power of the basic length a, and the unit vector direction or directions when appropriate. Answers in terms of generic Q1. Q2, etc. will not be acceptable; replace these generic (293 by the ones appropriate to the problem you are asked to solve. Please note that Q or it itseif is a positive quantity. The signs of the specific charges are specified separately. Constants and Conversion Factors: charge of electron(magnitude) or proton: e = 1.6 x 10'19 C Coulomb’s law constant: k6 = 1I4iteo = 8.99 x 109 (N-mzi’Cz) Permittivity of free space: so = 8.854 x 10“12 (CziN-mz) Use as the speed of sound in air: v = 340 mfs Minimum detectable sound intensity L, = 10'12 (Wlmz) 1. Two triangular wave pulses (shown below at some instant of time) are approaching each other. each at 3.0 crru's reiative to an observer fixed on the earth. Sketch the resulting disturbance 2 seconds after the time when the picture below was taken. Be sure to specify the location and size of the peaks, if any, and the width of the net disturbance. not. VP" AT t: 15 (pr-owl'- picture) H Alumna QuL foth inf 6 am i a-th‘l 2. The equation of a transverse wave propagating along a string with the disturbance in the y direction is given by y = 0.02-sin(8x — 40t) , where y is in meters, at is in meters. and t is in seconds. Determine the wavelength and frfluencx in Hz for this disturbance. (a) gig—:8 3;:3—1’wfi/tp— c.7354“ ..._..—.—.—._—~—--—‘ 8’ Us) QIr-f-z‘fo :7 i: £7.“ 2%. : 9:396 Hj‘ 3. For the same wave as in problem #2. determine the velocitv of propagation {magnitude and direction) and the maximum transverse velocity of the disturbance. 0"} 17': 40/8 r: 5411/5 iii +thr8etl5m Lb) WWW} box” : Lil-Maori = 0- B ”4/3 4. Write the equation for the wave disturbance that when added to the wave disturbance of problem #2 gives a standing wave with a node at x = O. ' 5 it vnl (1 my I t l VlLt. Y a: 0.3%?) Some {ft-dyytnty amt waflfl’lym W DPJOJ-LQ dwaci’leh 5. For the standing wave in problem #4, what is the maximum amplitude at the location of an antinode‘? )C'ms : 2 V 0' 09‘ W6” Cos C slot) £[O .06“ Ctfif‘f-Utflmx') mime-(Lt when sMCS’X!=j;i .: maxim-M ’3’ “#904 m 6. Sketch a picture of the third harmonic of a transverse standing wave disturbance on a strlng that is fixed at x = O and x :- l m, at the instant of time when the antinodes have maximum amplitude. If the velocity of propagation is 6 m/s. what is the freguenc! of the resulting standing wave? 7. Two speakers emitting the same displacement amplitude and frequency of snund face each other at a distance of 100 m apart. Midway between the two speakers is a location of an interference maximum. with intensity Im. If a sound detector is moved 0.34 m toward one speaker, and therefore 0.34 m away from the other speaker, then the intensity drops to zero. What is the frequency of the sound emitted by the speakers? 4- - _. first _ _. _. ._ was ‘55?“ 'fi 5' m [LL 2' D: 68 m . a. -1" # 3‘4—0 Wilhimfim AL:%: 0495’ -7;’;{" —- -——--' 2: 525!) Hg 1 t 5’ i9 k r: I . '3 e m z“ 8. If the fre uency of the sound emitted by the speakers in problem #7 is doubled, but the displacement amplitude of the sound waves emitted by the speakers remains the same, determine the approximate intensity of the sound at the offset position. [Hint Does the intensity change with frequency at the location midway between the Speakers? Does the interference pattern. as a function of position offset. change with I frequency?] Since (“Lemuel Ctr-giveaway fluent“; [03.147 H]? fi'fll‘lnll Wave ith’H‘) H“ §F¥5£f— Essif'xhn wt” 19a f-tlwenitnfll‘ Pail“; cliff-Keene? s‘a mkximvm E: Im fl): Lfrm 9. A point source of sound has a sound level of 15 dB when the observer is 15 m from the source. Determine the sound level in dfi when the observer is 5 m from the same source. {5 ‘16;- {0 £03.0(I Iél;‘m))- I5,__x _—__—, 16%“) (3.13%?)7luggw(yq) X A?) 2 E0 ’a’jte (Egg) X 7- ’f'f‘lopramfi) :15 +0.?5‘fxto x =2-‘L5‘l .. ,zLEs 10. You are standing in front of a bank that has just been robbed. One police car is leaving the bank area at 34 mfs in pursuit of the robbers. A second police car is approaching the bank at 34 mfs to check on the employees. Each police car’s siren emits a frequency of 700 Hz when it is parked in the garage. What is the beat frequency of the two sirens? '— ‘3: ‘ 3’" 0 ‘ ’ '7 70C,“ (ii-9:"— {iten}! 700 ( 3417+;LI) J fflpfnst‘sj 3‘110"3‘f) 1 — ‘ 0| 2 '- -— ' ..—-\' r' “"L '- ( ”Jr—J :TDUXW ‘kai‘ " 4'0.” Riven/4 750 I: (1" 0".) i f": I O I qq ”fleet = HIfl Hg 1 1. For the tour charges located at the corners of a square of side a shown below. write an expression for the force on a charge +Q iocated at the center of the square. (5%) iii-7+2 sadly—.2:— Vi 12. For the three charges shown b low, write an expression for the magnitude of the electric field at the point P(x=4a. y=33); and specify e direction of the electric field by an angle measured counterclockwise . r" a 2?" J23 lent 5/5 °-= MW: 180—3237;: 97. FEE-3" 13. For the two rings of charge shown below, writ—e— an expression for the electric field at the origin. % uh- E ?(+L‘)ffl.—-s—-_cp ‘11 v 7. (a 2+ “of/L ‘ 7" L .3) M ”L. _ .11 2 V3 E = new; .707) MM; 1 14. Referring to problem #13; if an observer is located far from the rings compared to their size, specify the dependence of the electric field along the x axis as a function of I x l , and specify the field direction both for positive and negative values of x. 1-6;! .flQ , . . .—, - I h“ Pv’nh rin'js links ll kc dIFOI-i (if, gate? 3:“ EXMETS field Pfiin‘h {*0 3H"? IE”: )(-.2) diéec'l'iéy, )5“ loci—L, PaSII’)—2 {tr-J “guild. U‘n‘ues (”0 [Wm-— 15. Consider the system of line charges shown below with charge per unit length 1-1 . If the magnitude of the electric field due to a single semicircular ring of charge with charge per unit length ?L and radius 3 is NZEEDR , write an expression for the magnitude and direction of the electric field at the origin. 16. Consider the system of a point charge and charged conducting shells as shown below. Write three expressions for the electric field at any distance r from the central point charge —Q in the three regions: 0 < r < a and 251 < r < 43 and 53. < r. Your expressions should be functions of g , not a , in this case. Cfihhvch “1+ 61“?" +2 Plant: Chm! e ‘- Q 0'4: 0911-") l 00/01.: G): ‘+T’tr‘*‘£’rr “(p/a: Er? - me w ' 22w <‘ia- @- wwrfl ewe/é; E“ r = 4* Weary» was: 5“ Y‘: (Q HIN“&"~“G 0+2?) «NJ/rs Fr : "QG/qfiafl 17. Referring to problem #16, determine the electric field in the two reWSa. £L<Y4<LJL Ha4r<55t f3: 0 f ; ‘3 C‘hQH-dfi‘ conical-Up 18. Referring to problem #16, determine the charge on the surface at r = a and on the surface at r 2 23. _, -— A _ ‘ _ 3”th E‘:Q 1h Inner “"1va J mysi, bird ‘I‘ @ Ohm-inné‘fi Svr’poqp mt Y‘.:&. ‘er éhhfifizfl'Qq+ “(if)” I BN1 LLnrJE L°n5o"vfl'h|o»,i mug!“ hwy-J + q) 0% Hi owl-kr- SVV‘RVL“ at Y'JQLL [Svm mv«i‘?llN {'le l9. Referring to problem #16, determine the charge on the surface at r = 4a and on the surface at r = Sa. Slncé 6:9 I»; Cit-544m f‘hJVL‘l‘UY; '1"th hmv‘i :Q HAIL I—-—---—-- Ch Hfl |thl fivrfilt‘F amt 1n_:qq: ‘l-m'a (”Hui (”Qi‘QQJIIHS‘JMVSvPI'Mf Bx] that“) Luxuzerui‘fic. J ”vii. 14‘“ ”2(1) at r35“. 20. A cubic cardboard box of side 53. is centered on the —Q charge. Using symmetry and Gauss’ Law, determine the electric flux through any one of the six sides of the box. sinc‘e ‘Hw. tormr of Ha? 59% is at a. radius Rb) RI: 3 d(2|5“}1+(-7.§4)Li Lara)?" = 512.51 = 4.33am) Then H'Ie they-7e enclaves]. EYH‘V-E’ox l5 (“Cp‘f‘Rqu’Jf Where cf :3 a. me u‘f’mfl mumhtr- and as Small Fae-titan )6 c‘p' 1% —c it Mai. new 5: rock—Hp ’ ’ .51th LY symmfnf )“he Saw flux 3943 Hum. each s? “”10 m w a... as. = How-Ba wt: liars? Hui-L113; In? I3 4.4.0.. on a... StalLJ-f‘hen answer“ 15 43/459 ...
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