13 Solved Questions on Introductory Physics I - Exam 1 | PHYS 6, Exams of Physics

Download 13 Solved Questions on Introductory Physics I - Exam 1 | PHYS 6 and more Exams Physics in PDF only on Docsity! Physics 6B Introduction to Physics IT Winter 2002 First Midterm Exam Print yourname: | Sylubu.. A Problems Maximum Score Score 1-6 24 18 20 9,10 12 11,12 24 13 20 Total (A) 100 Closed book; no notes; no calculators. All numerical calculations should be short and easy, but if you cannot quickly carry out by hand a numerical calculation (for example, a square root), then just express your result in terms of the various numerical factors, square root signs, etc. You may assume that any numerical constant provided in this exam is accurate to two significant figures. This exam includes 6 pages and 13 problems. It covers the first two homework assignments and through Section 20-5 of the textbook (lectures through the first half of the Jan 18 lecture). The following constants and equations may or may not be needed: Speed of sound in air: 350 m/s. Gas constant: R=8.31 J/mol-K Ratio of specific heat at constant pressure to that at constant volume, for air: y=1.4 Young’s modulus of steel: Y=20x10" Pa Average power transmitted by a harmonic wave of amplitude A and angular frequency @, ona string of tension T: P =1./uT@? A* a . 20, @ Wave equation: a -1% =0 dx* vor 1. (4 pnts) As the temperature of the air increases the speed of sound increases. _ aev b) decreases. Ue ” c) increases if the pressure is greater than 1 atmosphere and decreases if the pressure is less than | atmosphere. d) does not change. 2. (4 pnts) In which of the following gasses is the speed of sound the greatest? @ Hydrogen Justify your choice in one short phrase or sentence: b) Oxygen c) Xenon . d) Radon ( lightest molecule, ) 3. (4 pnts) Which of the following statemetits best explains why the velocity of sound is much higher in steel than in air? Je VON Hydrogen has the lowest malar Pas a) Steel is much more dense than air. The bulk modulus of steel is much higher than that of air. ¢) The wavelength of sound is much shorter in steel than in air. d) Steel has a much higher temperature than air. 4. (4 pnts) If functions f(x,/) and g(x,1) are both solutions to the wave equation and a and are arbitrary constants, then which of the following expressions also represent solutions to the wave equation? a) fa. eG.) . , ©) @ fd+b- aan Super esitiog grincigle co) fG.n? + gtr d) Ja-fan+o- gen 5. (4 pnts) Which of the following are not solutions to the wave equation for a wave of speed v = w/k , where fis an unspecified differentiable function? a) f(x-vt) b) A-expl-(¢-2/v¥ /2) @ At: eel d) A-sin(kx)cos(@t) 6. (4 pnts) A recorder is a musical instrument that can be thought of as a pipe open at both ends. Which of the following expressions represents the resonant frequencies of arecorder, where 7 =1,2---0o? a) f, = (2n-Lf, ® Ff, =f, hetm onic Series } f,=@2), d) f, = 2nf, th 11. (8 pnts) An electric guitar and a bowed violin both play a sustained A note, such that the fundamental frequency of the vibrating string in both cases is 440 Hz. Explain in general terms in one or two sentences why the human ear recognizes a different timbre (tonal quality) for the two instruments, allowing them to be easily distinguished even though they are playing the same musical note. The strengths of the Warr ous harmonies is different 4... the toe instruments. 12. (16 pnts) An organ pipe is 25 cm long. {a.) What is the fundamental frequency of a pipe this long that is open at only one end? (You may assume that an antinode is exactly at the open end of the pipe.) A= FR = | Om fit. LoOmh = 50H ro ).Om : (b.) What is the frequency of the first overtone from this pipe? Only odd Lacmontes wl! resonate, Se the Linst ever fone vs the. Sad harmonic. . {23 = 1050 Ha (she, +, cound ts V. Ne. Cie) 13. (20 pnts) A 0.020 kg string 2.0 m long that is fixed at both ends and under a tension of 100 N is vibrating in its fourth harmonic. The maximum displacement of any segment of the string is 2.0 cm. (a.) Graph the shape of the string when it is at its maximum amplitude of oscillation. (You do not need to draw a precise sine function, but do put the nodes and antinodes in the correct locations with the correct amplitude.) 4 T T T T r T T “bo o2 O.4 0.6 O.8 1.0 1.2 1.4 1.6 1.8 2.0 x (meters) (b.) What is the wavelength A of this standing wave? . 1 . Al ZB = { 3 m (c.) What is the frequency f of the wave oscillation? f-S 21 Tt o. Dow A aA » io 0.023 O.dr9 kA, on ~ ow f= ia ae loo Hh (d.) Write a wave function y(x,r) appropriate for this standing wave. ( costa also be pyverted ) glx t) = A wr In Ft on, 2 y A=L.ocm Le yoo the Cony phar in t de " hey (e.) What is the maximum velocity of the string at x = 0.25 m? « = 2¢ 4 Ot At x- OU wy 5g (x2 0am) = Tn fA = = - Uf A omtaft on Ex Mase. of Sinden ft = Feow on fs sim Ex =|