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Unformatted text preview: Probleml EXAW 1 Sﬂywinf) 2007—7. A stringed instrument is constructed by stretching a wire between two attachment Points (A and B) that are ﬁxed on walls (see ﬁgure). The walls are 3.50 m apart and the wire is stretched to a‘fension of 145.0 N. The speed of waves in the wire is 250 m/s. Calculate the following: (a) The linear mass density of the wire. (2 points) (b) The longest three wavelengths l1, l2, and R3 of waves produced by this instrument. Sketch the
modes (the spatial pattern that the vibrating string makes) that correspond to these three wavelengths.
(6 points) (c) The lowest three frequencies f1, f2, and f3 produeed by the instrument. (6 points) (d) The wavenumber k; and angular frequency 031 for the longest wavelength mode produced by the instrument. (4 points) In a completely separate situation, two waves (represented by functions W1 and W2) with the same wavelength are traveling in the same direction along a string. The ﬁJnctions representing the waves are: Wl (x,t) : (2.8 cm)cos(3.7x—4,5:) W2 (x,t) : (5.3 cm)cos[3.7x—4.5t+%] The arguments of the cosine functions are in radians.
(e) What is the velocity 17 (magnitude and direction) of the waves? (3 points) (i) What is the amplitude of the resulting wave W3 (x, t), where W3 (x,t) = W] (x,t) + W2 (x,t). Hint: use
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[3 X 312?5.3r99W/1 4. 5'1: glh'nr 121/],l1 CM Place your answers here: (2) (a) Linear Mass Density= Problem 2 Two sources of sound, SA and SB, emit sound equally in all directions. Each has a power of 135 W and emits sound waves with the same wavelength of 0.424 m. The two sources are in phase with each other. (a) What is the frequency of the sound waves? (4 points) (b) Neglecting 83, what it is the intensity of the sound waves from SA at point P1? What is the sound level
in decibels at P1 due to SA? (5 points) (c) The sound waves from SA and SB interfere at Point P1. What is the phase shift in radians between the
two waves? Is the interference perfectly constructive, perfectly destructive, or neither? (6 points) (d) The sound waves from SA and SB interfere at Point P; (which is halfway between S A and 83). What is the phase shift in radians between the two waves? Is the interference perfectly constructive, perfectly destructive, or neither? (6 points)
The two sources are now tuned to two different frequencies, with SA operating at wA=344 Hz and SB
operating at mg=348 Hz.
(6) A listener at P2 hears two new frequencies f1 and f2 that are different from 344 and 348 Hz. Calculate these frequencies. Hint: these two frequencies arise from adding cos(aJAt)+cos(a)Bt) and using the identity that cosa + cos B = 2 cos [ﬂat — ﬂ): cos [ﬂat + 5)] . (4 points) a) “p:— 22 gig .2335; LA )‘ ‘ LR Ll
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It: airmail: strin 1 wwww “WWf” O‘iUt’t/O‘SQ W‘wﬂ (“‘5 la? ‘05 664+ Place your answers here: Problem 3 A laser pointer produces light with a wavelength of 632 nm. The beam is collimated (neither diverging or converging) at a constant diameter of 1.50 mm and the intensity across the beam is a constant 2.803(103 W/mz. (a) What is the power of the laser? (4 points) (b) What is the amplitude (not rms value) of the electric ﬁeld wave in the laser radiation? What is the
amplitude of the magnetic ﬁeld wave in the laser radiation? (4 points) The laser beam is incident at Pt. A on the left side of wedged diamond window. The right side of the window is wedged at an angle 10° with respect to the vertical and the index of refraction of diamond is \ l a» L 2.424 a) I: 7%.. .9 Q: I A; : ﬂwmzmo3)vn(1:i3)
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M egg/“WE U1(7>?‘fc$}(if?éxlgl) (1'660X/a3) (c) Calculate the angle of incidence 0A at Pt. A with respect to horizontal so that the beam strikes Pt. B at
an angle of 244° with respect to the normal of the right surface. (5 points) (d) At what angle 63R with respect to the normal of the right surface does the beam reﬂect from the right
surface at Pt. B? (4 points) (e) What is the angle BET with respect to the normal of the right surface of the transmitted beam after it passes through Pt. B? (4 points» (i) If the angle of incidence at Pt. A is increased slightly (incident ray comes in steeper) from the value
that you calculated in part (c), what happens qualitatively to the ray that was reﬂected at Pt. B? What
happens qualitatively to the ray that was transmitted at Pt. B? (4 points) .,__._‘ C) 91: [$03100°—{75.L°:LW—° Iain 3: : KlL’FLS"H Mtge—‘9 6/3371935 OI) agar: fLJ—f'qo {Oh/w)“, m0 I‘P‘plotiiou 1 (inﬁll? ap'v’tﬂv’ﬂmt‘t) a) ham “UN 0: ram at; —9 9M we” i9; l 3) been will. 54r'pnf .NSML than n4 f». (a751,; (th’FQn/)om5’e (See dashed ‘9 WHO“: clPol bum. w H Pami ﬂown Maw" 1"; . #5)} )omol be H be br {n p'b‘)
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 Spring '08
 BERIM
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