test1 - Physics 112 Test 1 Physics for Scientists and...

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Unformatted text preview: Physics 112 Test 1 Physics for Scientists and Engineers Dr. Clark 13 February 2003 Do all problems. Show all Work and explain your reasoning to receive full credit. Do not use formulas or integrator features of calculators. If you do not understand a question or find it ambiguous, ask the monitor about it. A. Multiple Choice Problems: (8 points each) Circle the most correct answer. Box in your second choiCe for potential partial credit. 1. For a particular damped oscillator b/2m = 600, where b is the damping constant of the system with mass m and natural frequency (00. If the oscillator is let go from rest with some initial non-zero amplitude, it a. will oscillate without decay because b/2m = mg. b. will oscillate with a slow decay in oscillation amplitudes. (6) will simply go to its equilibrium position without oscillation. (1. will move toward its equilibrium position, but stop before it gets there. 2. The maximum LINEAR velocity of a pendulum with amplitude A and length L is 11' 1t 2/4 ‘69 “9+ propo mm o %\ g9: "(AA W: “A @ ALI/2. b. AL“. 0. AL . d.A1/2L. e. AZL. L6 = «AN—A“ 3* '13 7 VJ L A q H M = E » Ir = 5 EA 3. Two strings of different mass densities are tied together. One end is tied to a wall and the other a vibrator. Which of the following are true? a. There must be a node at the junction of the two sections of string/x)o b. The speed of the waves in the two sections of string are the same/v0 c. The amplitude of the waves in the two sections of string are the same. A10 d. The frequency of the waves in the two section of string are different. N0 (9 None of the above. 4. One wave carries twice the power of a second wave propagating in the same medium with the same frequency. The first wave has : L A 1) U)? SIN/*7. l7 2 P ‘- a. twice the amplitude of the second wave. P AD :1 g ‘ M . . P z z (’1 1 a b. a hlgher speed than the second wave. ' ’2. S L M c. a longer wavelength than the second wave. . \7 11 1.2 P}f 1’ w .L 7’ d. twice the speed of the second wave. W13» -. P Am :0 SM © between 1 and 2 times the amplitude of the second wave. , C M) 2:" 7' Z 7’ S7, M 5. Train 1 and train 2 have whistles that emit the same frequency sound waves when at rest. If they are travelling in opposite directions and away from each other, which is true? @ The frequency each hears for the other's whistle depends on how fast each train is going. w , b. Train 1 hears train 2's whistle at a higher pitch than when both are at rest. *’ ° 0. Both trains hear the other's whistle as the same frequency as their own. Na d. The frequency each hears for the other's whistle depends on how far apart they are. {v0 e. None of the above. N0 B. Short Calculation Problems: (8 points each) Show all work. 6. A wave on a stretched string is described by y] = A sin(kx - cot), and y2 = A sinflcx - cot + of). If the amplitude of the wave is 1.8 A, then what is the value of <1)? a M112 it; (flu aw M ewe-m mm: “LA 0" “a” -.\\"‘6 (w‘Wz ” ‘3'; :- Lap—i (O‘R5 7. A high—tech robot with a microphone is working its way through a cave as it searches for missing spelunkers. If the shouts from the spelunkers increase in loudness from 10’.10 W/m2 to 5.00 x 10'9 W/mz, after the robot has traveled 100 meters, how far from the spelunkers should the robot be? Assume spherical waves. :2 - Io 1% 7 0V 1' I - 0L _— a I\ (\ “— ‘L—l 1 (x v} A N :‘\(\'L: Elfi‘ PL A~\OOM c :L((\*°"B /____~. :\ ,, VS! loom 7:7. A r‘ W': Sim-aw“; _ (33’ ~ WSW \ |r_)"~""’l'l rt 8. The initial position of a mass on a spring is 2.00 cm from equilibrium in the direction of compression with an initial velocity of 0.400 m/s in the direction of compression. What is the phase of the cosine wave that describes the motion of the mass on the spring if the force constant a): 70.0 Hz? J 4&0 k \ ; W4 ‘F'wawOé—j X0 : 0.01M —-—U‘ i=0 M 2% X0 : aqoow‘lj _t " 0.900 5 04:5“! Z *M OIOZOM‘ - J WMW mmmmmmmmmmm ‘ Y1XW Cwa-E-hcp)’ “Mgr- 0‘7’7 2 Yuma I ' ’ “ ” ! 90%“1 q) X ’ 44) xvvwg-w - I o )L ~wxwgcwf‘t‘e‘x — lr- C‘ ’- ‘ .1... “Mr «t .» >v-‘iV-4' fl~w1m~>m~4 »- r , . 1:3,; v '- Q X M t f ,.VSW.....i . ._,..~.—AM-‘,—m 9. You measure the intensity of sound coming from a piano to be 10'9 W/m2 when a note at 1500 Hz is heard at a distance of 4.00 m from the piano. What is the amplitude of the 10. Two waves, y1= Asin(5.58x- 88.460 and y2= Asin(5.58x+ 88.46t), are traveling on a string of length 3.38 m which has both ends fixed (where SI units are used). Find the location of the first node (to the right of the left end of the string) for the standing wave that is the superposition of these two waves. Give your answer as a distance x from the left boundary. pg r Ll?- : Z A “($3 3 x) («to (38. H ht.) 4 J’ l k— ]— ~) SSQ'Lrn-fi, 30h If ‘ (5:595:59): “lg : )8. @JJmMLLME 3-3? n .— [5%é: é C. Full Problems: (20 points each) 11. A 2.5 m long pipe is closed at one end with a speaker attached, and your job is to determine if it is open or closed at the other end. Of course, you cannot see the other end, so you must use the speaker and a signal generator to find neighboring harmonics. The neighboring harmonics are at 266 Hz and 342 Hz. Is the pipe open or closed at the other end? You must justify your answer with calculations. What is the speed of sound in the pipe? What is the highest harmonic heard by an observer, whose hearing cuts off at 15000 Hz? What is the longest that the pipe could be if you cut off a section so that 266 Hz would again be an audible harmonic? Assume all values are known exactly. 5.5 ’ ’ ’ *3 '2 ff“ ” 2 (o ‘0 “2%; god: 3%” :31? . 7 (6 Hr? IIC WA!) — O " we «I z 5 ‘ JVC:V:\..P n;,l§/§7 £HVZL W JJ/ n. kt? [Lil T‘yctvi 3:51 :6: 29%:1 : 571:2 : QM “ 254, w B ‘1 t) 7/65 (film :Lanl ZUO 3am“ _LYH :) I, \ v :7 i,» “légn : .b {0‘ "I intaktr-we) {$014.0} 13% I vi 34;}, : 3g raj/j LN.ij V v 2(me ' in? t '76: m 312W mfig‘if‘rw‘n‘mwoku IQ - 24cm Q ’ 2 _ \6 7 x, a”; r ' $2 gar?” ,, m an? Wtiztrmtzstm : 3% lg V - Y\ J ,W , ; fl '7‘ ~:V;:j [(000‘4‘t- / WJMM fl L) WW) 312% V \ (aw/345W; /</fi3‘/ H1: 7 fl M H ~‘___'_.,___ Mr’dr-e " “me-r» 7.”, _<:>VH\U lemu‘i ( \}2 I t 2am L“, (gawk) WU : n ‘ L ‘ JJGWQ Amati/9M) / /6 12. A mass is connected to two springs with force constants k; and k2 as shown in the figure. The mass moves on a frictionless surface, is displaced from equilibrium and released. Begin with Newton’s second law and show that a solution of the form x = A cos(a)t+ ¢) yields a period. of m T=27r . kl+k2 Now calculate the acceleration for a 0.500 kg mass that is 3.00 cm from its equilibrium positionifk1 = k2 = 10.00 N/m. ...
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This note was uploaded on 03/12/2010 for the course PHY 112 taught by Professor Staff during the Spring '08 term at Illinois State.

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test1 - Physics 112 Test 1 Physics for Scientists and...

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