mt1solutions - Physics 113 ~ Fall 2011 First h‘lidterm...

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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.- 9} g . I”: .5. 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) row-Q 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 _ ébgLvl-r’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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