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Unformatted text preview: PHYSICS 2306 TEST #1
18 February 2000 16M0103 (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 (Nmzi’Cz)
Permittivity of free space: so = 8.854 x 10“12 (CziNmz)
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 (prowl' picture) H Alumna QuL foth
inf 6 am i ath‘l 2. The equation of a transverse wave propagating along a string with the disturbance in the y direction is
given by y = 0.02sin(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) QIrfz‘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” : LilMaori = 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 {ftdyytnty amt waﬂfl’lym
W DPJOJLQ 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‘fUtﬂmx') mime(Lt when sMCS’X!=j;i .: maximM ’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 Ctrgiveaway ﬂuent“; [03.147 H]? ﬁ'fll‘lnll
Wave ith’H‘) H“ §F¥5£f— Essif'xhn wt” 19a ftlwenitnﬂl‘ Pail“;
cliffKeene? 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,“ (ii9:"—
{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%)
iii7+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. FEE3"
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. 16;! .ﬂQ
, . . .—,  I
h“ Pv’nh rin'js links ll kc dIFOIi (if, gate? 3:“ EXMETS
field Pﬁin‘h {*0 3H"? IE”: )(.2) diéec'l'iéy, )5“ loci—L,
PaSII’)—2 {trJ “guild. U‘n‘ues (”0 [Wm—
15. Consider the system of line charges shown below with charge per unit length 11 . 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‘hQHdﬁ‘ conicalUp 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‘ @
Ohminné‘ﬁ Svr’poqp mt Y‘.:&. ‘er éhhﬁﬁzﬂ'Qq+ “(if)” I BN1 LLnrJE L°n5o"vﬂ'ho»,i mug!“ hwyJ + q)
0% Hi owlkr 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»; Cit544m f‘hJVL‘l‘UY; '1"th hmv‘i :Q HAIL I——— Ch Hﬂ thl ﬁvrﬁlt‘F amt 1n_:qq: ‘lm'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(25“}1+(7.§4)Li Lara)?" = 512.51 = 4.33am) Then H'Ie they7e enclaves]. EYH‘VE’ox l5 (“Cp‘f‘Rqu’Jf Where cf :3 a. me u‘f’mﬂ mumhtr and as Small Faetitan )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. = HowBa wt: liars?
HuiL113; In? I3 4.4.0.. on a... StalLJf‘hen answer“ 15 43/459 ...
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 Fall '06
 YKim
 Physics

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