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Unformatted text preview: Exam 1. Wednesday, February 18*, 2009 PHY 252 Name: SOLUTION Each question is worth 25 points. Answer three questions only. Be careful to justify your
answers — W Do not leave questions unanswered. Even if you cannot get the ﬁnal answer, show me clearly what you know. 1. A guitar string of scale length 629 mm is under a tension of 90. N. The string has a linear
density of 1.175 gim. The speed of sound in air is 344 m/s.
a. Determine the fundamental frequency of the string. (9 points) . . _ 2L. ..
Wave. velombd on SitInd U“ = Ji = {1, ’7‘  71"“l Vl j—or 13H: fundamentaL _
:E = *LJ? : I ‘10.”
2!. ,u. 2 x 0.62‘lm 1 Iii5' K 10—3 Kali” :5 : 22.0 H2. (Qéidjigs) ———————'—""'_"' 7“ A nearby organ has pipes that are closed at one end and open to the air at the other end. The
shortest pipe is 0.1 m, the longest pipe is 3.00 m.
b. What length pipe would resonate in its fundamental mode at this frequency? (8 points)
A stopped pipe. o§ length Lp Supports WQVe'eMd‘tL‘S
”A. = _ “‘11: and. n =o5or the fundamentaL, 1n+l For reacttance with fine guitar striﬂj ) maizkjrciuenahs =E=_U:_. L=¥=3IM+ =53: —_.._—_
j! 4‘ 441° _> P “'5 4x220 CHM ’9 Two guitarists simultaneously play the same sustained note — ‘concert A’ at 440.0 Hz — on
acoustic guitars. One of the guitarists is stationary with respect to you, while the other is
moving toward you steadily on a skateboard. You hear a beat frequency between the two
guitars of 2.0 Hz. 6. What is the speed of the skateboarding guitarist? (8 points)
. . ___‘ U" + U;
A I latener hears a. alopplerslufbecl freiaeucj :51.  ——— jig
u + v; Our listener 1; sia'ﬁieuaﬂ, so U;_=o, U; 'm nedq‘twg ECQRSC the Source '15 moving toward {low} and. so 5“ = :fc + ZOH; :51 = 59"”20 ‘= U '51: :3.) u; :. info U"
U‘—U_"_s *T
.L.
20 ~— 15 1; ml
U; _. x 341.»  6 mls own ﬂoat. “Jr2.0 7V 6—: Exam 1. Wednesday, February 18‘“, 2009 PHY 252 2. Your task is to design a guitar string made out of 1.00 g of steel of density p = 7800. kg/m3 . The steel will break if its tensile stress (force per unit area of string) exceeds 7.0 ><108 N/mz.
The guitar string is to be set to a tension of 90. N. Your job is the following: ,_ a. Determine the maximum length and minimum radius the string can have. (12 points) Mass M of sieei IL; ~— 17}sz : ’0—3K L : lendbk
M _ I a ' 3 Padi'us
:1Tr'1 = 1:55 9 :~. danish: 3 1 T = ‘bBuiswu Also siregg, \< $.me = 7.0xlo le.
I 'If'ri
Trrz >r : ... 1T1! = .91. a I.
5w“ L P snag _ 3
 . L \< ‘11:; 5mm: : 10 k3 ‘ 7Oxloaml...‘ = 05317“ = LCM Hale’
7 7,800 lulu? 90 M (25913 ﬁ3$ .) Clam ‘r’
and r' > ‘f = 0.000202 :
/ 11.5““ Tx7xlo’mm 0'20 MM h“ *’ b. Determine the lowest possible fundamental frequency for standing waves on the string,
assuming that the entire length of the string is free to vibrate. (13 points) H For the :fMMAaMGK'tGL ”A = 2L
‘ :5 :: “1— .1
' ' 21..“ # Buiﬁ: .3. :‘lTr‘P . _.._. _'. "LE TN In are
' ° use :5 2L WI Coastagd
. __ ‘l"
" 5' — \/4ML
' l __ Ill. 5M4].
loudest L. dives lowest 19' . .. Usg L— P ——T 15"?“ Glam 5:. r: .I. .91. ='. I... ._.
4"" “Sumac 2'” shut. 5. f: ‘iOJU 3.300 Rah“: «— ——'—r——
9 X '0 3kg Iona Mm: lowest IS" = ‘50 H2. Exam 1. Wednesday, February 18'“, 2009 PHY 252 3. Water stands at a depth H in a large open tank whose sidewalls are vertical. A hole is made in
one of the walls at a depth h below the water surface. <—R—>i a. At what distance R from the foot of the wall does the emerging stream strike the ﬂoor?
(12 points) The pressme at A is a‘tMospheric. presseue Po‘ Since 3 is opento digthe pressure a“: B is also Pa, Bernoailliis eiua‘b'ou :Icn— hand 8 '15 Po 1 P3” +0 =1 PO+PS(H“U+§LP”1
_ '_ 93k = fpvz => '1) = J22: hor'rzou‘bqflﬂ ‘ Tka time t for the Wa‘ter to fa.“ H—L is. found from 5: ‘4‘“: i311 => t= W
' — __ 2c) _ _
~ Mt @T—2WH* b. How far above the bottom of the tank could a second hole be cut so that the stream
emerging from it could have the same range as the first hole? (13 points) From aJAm R1 3 LrLUlk) . Tum 'm a. second—ma!” PD'ﬂhomiaL .m In, SO ”there is n. 5260144 3011?me Suppose £149. Satchel kale. is d from fine, IOO‘H‘OMJ'LLeu h=H._ﬂ_ * R1 = lr(H~3)(H—H+3) : HH—ula v TM, clear'3 d = L, ILS a. solution.
 . 52¢on hole aft 1163,11: lg fro.“ 100110;“ will also Jena! 0. siream adisiancc R Exam 1. Wednesday, February 18th, 2009 PHY 252
J) B 4. Two speakers, A and B are separated by a distance of 2.7 m along a y axis, and emit sound
waves in phase and at the same amplitude at a wavelength 090 m. A microphone is placed at
point P at coordinate xp on the x axis. What is the greatest value of xp at which detected sound is minimum due to destructive interference? (25 points) F07" destructive latchferencg theme Should be 6L hallf"
wavelength. path difference between Loaves arriving at P, A DC. A’A. = (Mela = BP—AP r1=fnb er M7;
(mm = dive — cap ‘d B 0‘ (ninth +39. = v(al2+x;)
'2.
[CMéJa +121 T‘— 4.2+ 33 Wpedn'on ~19 is largest when n20. (Increasing M decreases the numerator, and harass the
danomina‘ton) . '_ 92'. d1 “' “3/4! :: (2'?M)1' (0'9“)2/9.
aim“ 7* (OHM) ll x? = Vacl m ' .
9. Strings ...
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