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Unformatted text preview: 1. What is the phase constant for the harmonic oscillator with the 1)
acceleration function a(t) given in diagram if the position function a (m/ 5—)
x(t) has the form x(t) = A cos(a)t + (15) . Answer in Radians _: ‘ “W 4' ” (a) 0.91 @ (c) 2.61 (d) 3.14 (e) 4.46 L; 9.4,. A” a(0)==+””/J"
ﬁw‘é‘mqﬁj— ﬂwlsammw : 9 3.(m(¢/= 04mm WA Wa arcaéra/m 4a; man/W i q/agym max” 4' 49¢me .
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4* 2. Two springs with one with force constant k1 and the other with
force constant k2 have one end attached to a ceiling and the other
to a mass of 1 kg as shown in diagram. They are both pulled 
0.01 cm from equilibrium and released from rest. After 10 seconds
spring of k2 has completed_ 0_ne more oscillation than k1 If k1: 5 N/m
ﬁnd k2. Answer 1n N/m (b) 7.1 (c) 6.0 (d) 4.1 (6) none of these
’7‘ .. 277 in aw»! ’72. ; 27} M A
/' ' Kt! k1. W 'n MM/A‘ 72¢ WA»? area/Ari 59/ Physics 125 Midterm — Winter 2006 ‘7 Page 3 of 10 3. The mass pulley system is in equilibrium as shown in
diagram. At equilibrium the spring has extended some
“x0” units from its unstretched position. If the mass “m ”
is pulled a certain distance “x ” from equilibrium and rmeleased
from rest the system would produce simple harmonic motion
If the mass is 10 kg and the spring constant is 98 65 N/m (Assume both pulleys are massless) ﬁnd the period of oscillation.
Answer in sec. ‘ (a) 4.1 (b) 3.2 '(c) 2.2 (e) .49 ﬁg '5‘ M —0 __® $ r
3f ﬂmf :ﬁﬂ/nfchZIal Am “@4110 8: he mﬂ‘w/ 1'14 ¢0S4$w T—k9«o= 0 “C9 . jam [email protected]_ 7:9: ”95/2,: ——®
(”MK/a“ mamw aéu/y/mimé x méddm Ayaléé’nwm ZF ma /nm“’” 47+“
”99,9.7‘: ”9052}?! ”IQMJAM W444 29‘ :g/ﬂammv/ﬂluw %" WA 7!“ 9/94 7': (“o+1%)k . Mj”2k(%o+2—°‘): ”’43": 23' .. k A 5A!"
_ 5522: __,L 772.1249 ~9:x] =7 54,—? “4%)94 >
J: 'M __ 2/00‘c ‘. w : (/23? : 31’ == = grail}; '— 2.7 9499559 2
m 7— A 0 \
4. A physical pendulum has been created the following way. Arpoint metal mu 8 Z
mass (mud ball) of 0.75 kg is attached to one end of a rod ofjength T 9.1
1 m and mass 1 kg and a uniform disk of mass 2 kg and radius 0.25 m ~ 0 to the other end. If it is pivoted at a point 0.25 m from the pOint mass l
and made to oscillate in small angle it will produce simple harmonic ;
motion. Find the period of oscillation. Answer in sec. . . l
I
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(21) 5.12 (b) 4.19 (0)3.12 (d) 2.23 (e)“none ofthese Physics 125 Midterm — Winter 2006 f Page 4 of 10 5. A strange wave on a string can be described as y = 2e3x (X,‘y are in meters). The wave is
moving in the positive direction with some speed v. It is found that the transverse speed of
a particle at x = O and t = 0 is 30 m/s. If the string has a linear density of2 kg/m calculate
the tension of the string. Answer in newtons. (b) 60 (C) 70 (d) 80
3C%,U’€) 0C 3vb] (e) ‘90
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pox—12¢): 2e gym/cl :2[e e 6
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‘1? 6. A harmonic transverse wave is moving in the positive x direction. At t = O and x = 0 the
transverse displacement is 2cm and the transverse velocity is positive. If the wave
amplitude is 4 cm ﬁnd the phase constant. Answer in radians. (a)0.52 (b)2.625 (d)4.19 (e)5.76
tyl'mc): ”444(kx'w61‘7ﬂ) _.. ”a 40
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at“) (a ewe—Huey) Physics 125 Midterm — Winter 2006 ‘ _ Page 5 of 10 7. Two harmonic travelling waves y1 : A sin(kx — cot) y2 = Asin(kx — a)! + ¢) are moving on a long string. They interfere to produce a resultant amplitudeof 1.93 A. Now if the
direction y; is changed ﬁnd the maximum transverse displacement of a particle at x = 0. (a) 2.09A (b)1.05A ((00.5%) (d) 0.26A t1 ii:(‘e)noneofthese ycy/ fig, W [VicMfg [,1 52 :4 ICﬁm ‘—
3/: RACﬂ(W;/W(Axwf+¢/Lj, §?Z
[email protected]¢/z):/93>ﬂ _f: 053?“ Wx— J L. a.
may (1/,: AwCE “’6 49)} 3.:7’l‘y y, 2 AW (knownf j {fl/4&0!“ +¢A)Cw(w6+§4
‘  = 1/4424 z). : 0r2/f
VZV%W( ﬂ“ mew— dzo/o ed vac—0 D ‘ 97 z: 8. Two sinusoidal waves of the same period, with amplitudesoslC 5.0 mm and 7.0 mm, travel
in the same direction along a stretched string. The resultant amplitude they produce is l 1.6 mm. If the phase constant for the 5.0 mm wave is 15°. Calculate the phase constant for the
7.0 mm wave. Answer in degrees. (a) 30 (c) 150 (d) 165 I i (e) none of these Physics 125 Midterm — Winter 2006 Page 6 of 10 9. An organ pipe A (one end closed) and organ pipe B (both ends open) have lengths L A and
LB. A certain frequency sets up a 3rd harmonic in pipe A ‘(n z 3) and a 6th harmonic in Pipe
B. If pipe A is 0.5 m in length ﬁnd LB. Answer in (m). ‘ (a) 0.25 (b) 0.5 (c) 1.0 (e) 4.0 ________________,___. k,” “—2). 4—lrs 7’.”
1%; J23;— W, Fr» YEW; .
’fmgf” 7? 6%; :lﬁﬂ ’ L/b : ‘ILﬁ 2 7025) Lg 10. ﬂ The sound source of power “P” watts produce a sound level: of 70 dB at a certain point. If
the power of the source is increased by 40% by what percentage will the sound level increase at this pomt? .7
, 39/
(a) 1.60% (b) 2.08% (c) 16.8% (d) 20.8% : A (e) 40.0% “—1049; if: f: z _'./ﬂgM:W/«¢oym
” ,4,” ;}.‘§;4mw/{7 M m
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,0 A; /% W inwkavf‘of Physics 125 Midterm — Winter 2006 i Page 7 of 10 11. A detector (1 cm2 area) measures the sound level from a point source 50 m away to be 100
dB. If the detector is now placed at 70 m from the source what is the power passing through the detector. Answer is ,uW (1 #w = 106 w) i A
(a) 2.57 (b) 1.38 (c) 0.92 (e) 0.32 159; 70 ﬁ‘ad fwféaﬁ.‘ 59% 72¢: S‘OM Piaf ‘ C19,)
[00 = 10 47 to :73: by 15., = mag Ia (0’4” , ~ 1. ‘
15°  [0 IO . .‘ T50 ; (/0’v(r05_{1/.= I0 W/M ‘L
I d. W MM / i .
W’” ‘1 or :2: (5. (om/o ‘J W
190 = (5 ——7 '7‘° '7‘ 12. Two sound sources (each producing a sound of wave length k in phase)
are separated by a distance 2.57» as shown in diagram. If a detector is moving along the circumference of a large circle surrounding the sources how many interference maxima (constructive interference) are detected 3
in one full circle. (a) 4 (b) 6 (c) 8 @g :(e) 12 Q/f A 7);... ﬂﬁ'ﬂ We. :0 m4 M f); u H n = 2.5.? MW'
”(/wu ﬁfe/b :5 0,0,2?) ﬂaggw/(LM 33
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$40 A .7.) 21 1'9 M /—'— (‘ﬁ Physics 125 Midterm — Winter 2006 V Page 8 of 10 13. A listener at rest (with respect to the air and the ground) hears a signal of frequency f1 from
a source moving toward him with a velocity of 16 m/s. If thellistener then moves toward the approaching source with a velocity of 25 m/s, he hears a frequency f2 that differs from f1 by 37 Hz. What is the frequency of the source? (Take the speed of sound in the air to be
340 m/s.) Answer in Hz , ' (b) 510 (c) 600 (d) 620 * (e) 706
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