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Unformatted text preview: Physics 113 ~ Fall? 2011 First h‘lidterm Exam ~ Wednesday; October 19, 2011 The exam lasts .50 minutes. You may consult both sides of a single 3” X 5” notecarclt otherwise
the exam is closed book and closed notes. A calculator may be used for graphing and
calculations. Show ail your work in order to receive credit for your answer. Include the correct units on
numerical answers, indicate the direction of vector quantities, and clearly indicate your ﬁnal
answer. Do not begin the exam until everyone is instructed to do so. Your signature below indicates
your adherence to the Universityis policies of academic integrity. The exam consists of three problems. @{L {Mfg 5: a <} 31’ Name: Signature: Student ID #: Question Number Maximum Points Points Earned , +
g 1 30
w r t + 1
ieee 2 30
{:emee 3 30
Total: 90 ”V 3 , 1. A pipe lies along the naxis and has a length L. The pipe is dosed at :1: z 0 In and
open to the air at 3: x L. ::
r———————+;x Standing sound waves in the pipe are described by Apﬁzg t) z: A sin (k3: + (2’)} cos wt, Where Ap is the pressure variation from atmospheric pressure. At t 2 0 S, the pressure variation at the Closed end 333(2: 2 0,25 3 0) 2 330. (an) Give an approximate numerical value for w/k. wig? Z Vie ﬁt“ iﬁii Wig (1).) Determine the unknown quantity A. @ ﬁio ? eegéeegieg ewe 5%? :2: % we £1: E (6.) Determine the unknown quantity g5. ((1.) Find an expression for k gegi’we; meme? gas iiime 2. A mass m is held from above by a spring with force constant k and immersed into a
cup of water. Suppose the water applies a damping force —b17, where b is a positive
constant and 17 is the velocity of the mass relative to the liquid. an
I u r.
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g .
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ii '' (a ) The cup of water is at rest What is the angular frequency of the mass oscillating in the water? ?W)2
allaMPQQ 0&1}:wa ) (A) i: S 1% _CZ~E)L The cup of water now oscillates vertically, where the position of the bottom of the
cup is given by d(t) = D cos wt. (h) Write the differential equation (Newton’s 2nd Law) which describes the mass’s
motion from equilibrium :1:(t). 6 ‘ Mg: '7:— ~kx ,. Ev blew; V“Z X~ol
1: w er bit  LDLQ shut t X + Dwﬁkii 7:) 91M [ﬁvfgw + Covakyuzi oscillilwn w/ F60 ‘3 » WU SM (0 ) As the cup oscillates, what is the angular frequency of the mass? (gerrM? Rel “MAILI 'i‘LL 056“ “l“?ﬁ QR Z « ((1.) As the cup oscillates, what is thea (gm: litu e of the mass? “PM we“? L) AHA) rowQ i‘; loved =1:
:2 A Mi: é“) +914“ \0 \O \l} 3. A pair of 100 W speakers are in phase and both produce sound at 500 Hz. Each speaker
acts as a source of spherical sound waves. The speakers are separated by a variable distance .3. A listener is located at point P, :1: = 2.00 in directly in front of speaker B
(see ﬁgure). (31.) Find the smallest s for which the thensity reaches the listener. inﬁJm/L \L _
ébgLvlr’kbk AAA“ acct/M QM“ fax—L m 0Q V\%‘: ﬁnally“ :ﬂs +10 ”X :2 O’H‘lM :17 7;: (21M (b.) What would be the intensity at the listener from speaker B alone? ,.. _ ..._ PB mow
11m)... ,......,,_ .. WM.) “tax
1: ma “/wc (c ) Find the next highest frequency above 500 Hz for which the listener receives max—
imum sound intensity. Assume the speakers are at separation s from part( Lgdecl‘M 3A" occur; RV” XL )(t: W7? ...
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