This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 nonzero 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 ewem 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': Simaw“; _ (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 CwaEhcp)’ “Mgr 0‘7’7 2 Yuma I ' ’ “ ” ! 90%“1 q) X ’ 44) xvvwgw  I o )L ~wxwgcwf‘t‘e‘x — lr C‘ ’ ‘ .1... “Mr «t .» >v‘iV4' 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'Lrnﬁ, 30h If ‘ (5:595:59): “lg : )8.
@JJmMLLME 33? 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 intaktrwe) {$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’dre " “mer» 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. ...
View
Full Document
 Spring '08
 Staff
 Physics, Wavelength, frequency sound waves, initial nonzero amplitude, particular damped oscillator

Click to edit the document details