Q1. A transverse sinusidal wave travelling n a string is given by: y (x,t) = 0.20 sin (2.5 x 80 t) (SI units). The length f the string is 2.0 m and its mass is 1.5 g. What is the magnitude f the tensin in the string? A) 0.77 N B) 0.24 N C) 0.63 N D) 0.31 N E) 0.86 N v = ω k = 80 = 32 m/s 2.5 v = τ µ v2 = τ µ τ = µv2 = 1.5 10 3 2.0 (32) 2 = 0.77 N Q2. Tw pulses having the same amplitude and the same speed v = 1.0 cm/s apprach each ther, as shwn in FIGURE 1, which shws their psitins at time t = 0. At what time will they cmpletely cancel each ther? Fig# 1 A) 5.0 s B) 1.0 s C) 3.0 s D) 7.0 s E) 6.0 s The distance between the centers f the pulses is: d = 13 3 = 10 cm Every pulse has t mve a distance x = d = 5.0 cm 2 t = x v = 5.0 1.00 = 5.0 s
Term: 113 Sunday, July 01, 2012 Page: 1 Q3. A string with a length f 2.50 m has tw adjacent resnances at frequencies 112 Hz and 140 Hz. Determine the wavelength f the 112 Hz resnance. A) 1.25 m B) 1.00 m C) 5.00 m D) 2.50 m E) 1.67 m Q4. f 1 = f = 140 112 = 28 Hz f n = nv 2L = nf 1 n = f n f 1 = 112 28 = 4 λ n = 2L n λ 4 = 2L 4 = L 2 = 2.50 2 = 1.25 m A string f length L, mass per unit length µ, and tensin τ, is vibrating at its fundamental frequency. If the length f the string is dubled, with all ther factrs held cnstant, what is the effect n the fundamental frequency? A) It becmes ne half as large. B) It becmes tw times larger. C) It becmes 2 times as large. D) It becmes 1/ 2 times as large. E) It des nt change. f n = nv 2L f 1 = v 2L = 1 2 τ µ. 1 L τ and µ are ixed f 1 1 L if L is dubled, f 1 is halved.
Term: 113 Sunday, July 01, 2012 Page: 2 Q5. Tw speakers (A and B) are driven by the same scillatr with a frequency f 172 Hz, and are separated by 10.0 m, as shwn in FIGURE 2. A persn starts at A and mves tward B alng the line jining the tw speakers. At what distance frm A will he bserve the first minimum? Take the speed f sund t be 344 m/s. Fig# 2 L 1 = x, A) 4.50 m B) 9.00 m C) 4.00 m D) 8.00 m E) 2.50 m L 2 = L x x L- x L = L 2 L 1 = L x x = L 2x First minimum: L = λ 2 λ 2 = L 2x 2x = L λ 2 x = L 2 λ 4 = L 2 v 4f = 10 2 344 4 172 = 4.5 m Q6. The sund intensity at a distance f 16.0 m frm a sund surce is 0.250 W/m 2. What is the sund level at a distance f 28.0 m frm the surce? I 1 = A) 109 db B) 112 db C) 114 db D) 105 db E) 119 db P s 4πr 1 2 P s = 4πI 1 r 1 2 β 2 = 10. lg I 2 = 10. lg I 0 4πI 0 r 2 2 = 10. lg 4πI 2 1r 2 0.25 256 = 10 lg 4πI 0 r 2 2 10 12 = 109 db 784 P s
Term: 113 Sunday, July 01, 2012 Page: 3 Q7. A sund surce emitting sund with a frequency f 400 Hz is placed at the entrance f a tube that is attached t a mving pistn, as shwn in FIGURE 3. Hw many resnances can be heard as the pistn is mved t the ther end, which is a distance f 1.00 m frm the entrance? Take the speed f sund t be 344 m/s. Fig# 3 A) 2 B) 1 C) 3 D) 4 E) 0 f n = nv 4L L n = nv 4f = n 344 4 400 = 0.215 n L 1 = 0.215 m within the tube L 3 = 0.645 m within the tube L 5 = 1.075 m utside the tube Q8. Tw cars have hrns that emit sund with a frequency f 396 Hz. The cars are traveling tward each ther, each with a speed f 9.00 m/s. What frequency d the passengers f the cars hear? Take the speed f sund t be 343 m/s. A) 417 Hz B) 396 Hz C) 375 Hz D) 406 Hz E) 423 Hz f = f. v + x {x = speed f cars, v = speed f sund} v x = 396 343 + 9 = 417 Hz 343 9
Term: 113 Sunday, July 01, 2012 Page: 4 Q9. A steel rd is placed between tw parallel walls, as shwn in Figure 4. At 20 C, the rd has a length f 3.5 m and is separated by 1.0 mm frm each wall. The rd is heated unifrmly. At what temperature will it tuch bth walls? The cefficient f linear expansin f steel is 11 x 10-6 C -1. Fig# 4 A) 72 C B) 52 C C) 42 C D) 62 C E) 82 C L = αl T T = L 2 1.0 10 3 = αl 11 10 6 = 52 C 3.5 T f = T i + T = 72 C Q10. A 1.0-kg f ice at 0.0 C is added t 1.0 kg f steam at 100 C. When thermal equilibrium is achieved, what is the final temperature f the system? A) 100 C B) 0.0 C C) 50 C D) 15 C E) 85 C Heat t melt ice and heat t 100 C Q i = m i L f + m i c w T = (1.0 333) + (1.0 4.19 100) = 752 kj Heat gained frm steam if it cndenses Q s = m s L v = 1.0 2256 = 2256 kj Since Q s > Q i : ice melts and heats t 100 T f = 100
Term: 113 Sunday, July 01, 2012 Page: 5 Q11. Cnsider the cyclic prcess shwn in FIGURE 5. If Q BC is negative and ( E int ) CA is negative, which f the fllwing statement is CORRECT? Fig#5 A) Q AB is psitive B) QAB is negative C) QBC is psitive D) QCA is psitive E) Qnet = 0 Cyclic Prcess: Q CA = E CA + W CA W net = Q net + = Q AB + Q BC + Q CA ( ) Q CA is ( ) ( ) + =?? +( ) + ( ) Q AB is (+) Q12. The walls f a cntainer have a thickness f 2.00 cm and are made f a material that has a thermal cnductivity f 0.0300 W/m.K. The ttal surface area f the cntainer is 1.20 m 2. If the cntainer is filled with 4.00 kg f ice at 0.00 C, and the temperature utside the cntainer is 20.0 C, hw lng des it take the ice t cmpletely melt? P cnd = A) 10.3 hurs B) 4.22 hurs C) 17.6 hurs D) 22.1 hurs E) 13.6 hurs k. A. T L = 0.03 1.2 20 0.02 = 36 W Q = ml F = 4.00 333 10 3 = 1.332 10 6 J But P cnd = Q t t = Q P Cnd = 10.3 hurs
Term: 113 Sunday, July 01, 2012 Page: 6 Q13. Cnsider tw cylinders, ne filled with xygen and the ther filled with nitrgen. If the gas mlecules in the tw cylinders have the same rms speed, which f the fllwing statements is CORRECT? [mlar masses: M O2 = 32 g, M N2 = 28 g] A) The temperature f nitrgen is less than the temperature f xygen. B) The temperature f nitrgen is greater than the temperature f xygen. C) The temperature f nitrgen is the same as the temperature f xygen. D) The average kinetic energy per mlecule is the same fr the tw gases. E) The average kinetic energy per nitrgen mlecule is greater than that f an xygen mlecule. V 0 2 = 3RT M 0 T 0 M 0 = T N M N V N 2 = 3RT N M N T 0 T N = M 0 M N > 1 Q14. A 2.0-ml sample f an ideal gas, at 0.0 C, expands isbarically t twice its riginal vlume. Hw much wrk is dne in the prcess? A) 4.5 kj B) 2.3 kj C) 6.8 kj D) 5.7 kj E) 3.5 kj W = p V = p(v f V i ) = p (2V i v i ) = pv i = nrt i = 2 8.31 273 = 4.5 k J
Term: 113 Sunday, July 01, 2012 Page: 7 Q15. A 2.00-ml sample f an ideal mnatmic gas expands adiabatically frm a temperature f 300 K and a vlume f 12.0 L t a final vlume f 30.0 L. Hw much wrk is dne in the prcess? A) 3.42 kj B) 5.70 kj C) 1.14 kj D) 7.98 kj E) zer T i V r 1 i = T f V r 1 f T f = V r 1 i. T V i = 12 5 f 30 3 1 300 = 163 K adiabatic: Q = 0 W = E int = nc v T = nc v (T f T i ) = 2.00 1.5 8.31 (163 300) = 3.42 k J Q16. An ideal gas is cnfined in a rigid tank (cnstant vlume) at a pressure f 12.0 atm and a temperature f 25.0 C. If tw-thirds f the gas is withdrawn and the temperature is raised t 75.0 C, what is the pressure f the gas remaining in the tank? A) 4.67 atm B) 9.34 atm C) 12.0 atm D) 24.0 atm E) 42.1 atm p i V i = n i RT i p f V f = n f RT f p f p i. V f V i = n f n i. T f T i p f = n f n i. T f. p T i = N/3 i N 75 + 273. 12 = 4.67 atm 25 + 273 Q17. The initial state f a mnatmic ideal gas is represented by the dt in FIGURE 6. Arrws 1 thrugh 4 represent isbaric, isthermal, and ischric prcesses that the sample can underg. Which prcess crrespnds t the highest increase in the entrpy f the gas. Fig# 6 A) 4 B) 3 C) 2 D) 1 E) All prcesses are the same
Term: 113 Sunday, July 01, 2012 Page: 8 Q18. A heat engine is cnnected t tw heat reservirs: ne is steam at 100 C, and the ther is ice at 0.0 C. The engine runs by cndensing 1.0 g f steam and melting 5.0 g f ice. What is the efficiency f this engine? A) 0.26 B) 0.74 C) 1.0 D) 0.35 E) 0.65 Q H = m s L v = 1.0 10 3 2256 10 3 = 2256 J Q L = m i L F = 5.0 10 3 333 10 3 = 1665 J ε = W Q H = Q H Q L Q H = 1 Q L Q H = 1 1665 2256 = 0.26 Q19. A cup hlding 125 g f ht water at 100 C cls t rm temperature, 20.0 C. What is the change in entrpy f the rm? Neglect the specific heat f the cup. A) + 143 J/K B) + 154 J/K C) 143 J/K D) + 1.01 kj/k E) 1.01 kj/k Heat lst by water: Q = mc T = 0.125 4190 80 = 41900 J The rm is a thermal reservir: S Rm = Q T = 41900 = +143 J /K 20 + 273
Term: 113 Sunday, July 01, 2012 Page: 9 Q20. During each cycle, a refrigeratr expels 625 kj f heat t a high-temperature reservir and takes 550 J f heat frm a lw-temperature reservir. What is the cefficient f perfrmance f the refrigeratr? A) 7.3 B) 2.1 C) 8.3 D) 1.1 E) 1.9 W = Q H Q L = 625 550 = 75 J K = Q L W = 550 75 = 7.3