Phys0 First Major-6 Zero Version Coordinator: Saleem Rao Sunday, March 9, 07 Page: Q. A transverse wave travelling along a string (x-axis) has a orm given by equation y ym sin( kxt). FIGURE shows the displacement o string elements as a unction o x. Find the angular wave number k o the wave. A). m - B) 0.70 m - C) 4. m - D) 3.0 m - E) 9.0 m - Figure k.094 / m 3 Q. FIGURE shows the transverse velocity u versus t o the point on a string at x = 0 cm as a sinusoidal wave passes through it. Find the amplitude ym o the wave A) 5.5 cm B) 40.0 cm C) 5.0 cm D). cm E) 80.0 cm umax ym From the graph u max 0.4m / s.57 T rad / 4 s Thereore 0.4. 57 y m y m 0.55m 5. 5cm Figure King Fahd University o Petroleum and Minerals Physics Department c-0-n-0-s-0-e--g--o-0
Term: 6 Sunday, March 9, 07 Page: Q3. What phase dierence, in terms o wavelength, between two identical traveling waves, moving in the same direction along a stretched string, results in a combined wave having an amplitude.50 times that o the common amplitude o the two combining waves? A) 0.3 B) 0. C) 0.50 D) 0.70 E).50.5ym y m cos /.5 cos / o 4.4 8.8 80 = λ 8.8 = 8.8 80 λ 8.8 = 0.3 λ Q4. A vibrating source generates a sinusoidal wave o constant requency in a string under constant tension. I the power delivered to the string is doubled which o the ollowing statements is TRUE? (v is the wave speed and ymis the wave amplitude) P v yma ymb P 4 A) v remains constant and ym increased by a actor o. B) v decreased by a actor o and ym is increased by a actor o. C) v increased by a actor o and ym is decreased by a actor o. D) v remains constant and ym is decreased by a actor o. E) v remains constant and ym is increased by a actor o. avg y m A P B v = τ ; μ = constant, τ = constant μ v = constant
Term: 6 Sunday, March 9, 07 Page: 3 Q5. A string ixed at both ends is under a tension o 360 N. One o its resonance requencies is 375 Hz. The next higher resonance requency is 450 Hz. What is the undamental requency o this string? A) 75.0 Hz B) 300 Hz C) 5 Hz D) 43 Hz E) 50 Hz nv nv 375 n L L ( n ) v nv v n 45 L L L n n 45 375 v 75 L v L Q6. Two in phase point sources S and S placed 4 m apart emit identical sound waves o wavelength m. A detector placed at points P, P, and P3along the line joining SSshown in FIGURE 3, will detect Figure 3 A) maximum intensity at all three points P, P, and P3 B) maximum intensity at P and minimum intensity at both P and P3 C) minimum intensity at both P and P, and maximum intensity at P3 D) maximum intensity at both P and P3, and minimum intensity at P E) maximum intensity at P and minimum intensity at both P and P3 A path dierence or all point p, p, p 3 is s s s s = 4m = λ
Term: 6 Sunday, March 9, 07 Page: 4 Q7. A two-open ends pipe is 78.0 cm long. Third harmonic o the two-open ends pipe is equal to undamental requency o a one-open end pipe. How long is the one-open end pipe? n, open n, open, open v ' ' 4L L A) 3.0 cm B) 6.0 cm C) 34.0 cm D) 78.0 cm E) 56 cm 3v nv L nv 4L' 3,open ' L 3 78 l L 3cm Q8. A spherical point source radiates sound uniormly in all directions. At a distance o 0 m rom the source, the sound intensity level is 80 db. At what distance rom the source is the intensity level 60 db? A) 0.0 km B) 00 km C) 0.0 km D) 0. km E) 0.0km β = β β = 0 dblog I I 80 60 = 0 dblog P s 4πr P s 4πr = 0dBlog ( r r ) = log r (0) 0 = r (0) r = 0 4 r = 0 = 00 m = 0.0 km
Term: 6 Sunday, March 9, 07 Page: 5 Q9. A car is travelling rom a stationary observer A towards another stationary observer B, as shown in the Figure 4. The observer A hears a sound o requency 747 Hz and the observer B hears a sound o requency 863 Hz rom the car horn. How ast is the car traveling? Figure 4 A) 4.7 m/s B) 46.0 m/s C) 50.4 m/s D) 0.0 m/s E) 75.6 m/s 747 = V V + V c ; 863 = V V V c 747 863 = V V+V c V V V c 747 863 = V V c V + V c 863 V 863 V c = 747(V + V c ) 863 V 747 V = 863 V c + 747 V c 863 747 863 + 747 V = V c 6 66 V = V c V c = 6 343 = 4.7 m/s 66
Term: 6 Sunday, March 9, 07 Page: 6 Q0. Q. On a linear X temperature scale, water reezes at 0.0 o X and boils at 360.0 o X. On a linear Y temperature scale, water reezes at 70.00 o Y and boils at 30.00 o Y. A temperature o 50.0 o Y corresponds to what temperature o X scale. or Y 50 A) 30 o X B) 0.00 o X C) 440 o X D) 45.0 o X E) 560 o X X MP Y MP BP MP BP MP X ( 0) Y ( 70) 360 ( 0) 30 ( 70) X 0 50 ( 70) 480 30 ( 70) 0 40 X 0 30 5 g o a metal at a temperature o 5.0 o C is dropped into a thermally insulated 5 g copper container containing 35 g o water at 98.0 o C. A short time later, the system reaches its inal equilibrium temperature o 78.0 o C. Find the speciic heat o the metal (speciic heat o copper 400 J/kg.K) X A) 900 J/kg.K B) 645 J/kg.K C) 788 J/kg.K D) 00 J/kg.K E) 440 J/kg.K Heat lost = heat gained mc T water mct Al mct metal 0.35 490 0 0.5 400 0 0.5 c(63 water Al metal 735 water 800 Al 3.56c metal c 9035/3.56 900J / kg. K
Term: 6 Sunday, March 9, 07 Page: 7 Q. When a system is taken rom state ito state along path iain FIGURE 5, Q = 50 cal and W = 0 cal. Along pathib, Q =36 cal. What is W along path ib? Figure 5 A) +6.0 cal B) +66cal C) +0 cal D) 6.0 cal E) +3.0 cal E int Q W Change in internal energy or ia and ib is same Q W ia Q W ib 50 0 36 W W 6. 0cal Q3. A cylindrical copper rod o length 0.800 m and cross sectional area o 8.00 cm is insulated along its side. One end o the rodis held in a water-ice mixture and the other end in a mixture o boiling water and steam. Calculate how much ice will melt in 0.0 min in the ice-water mixture (assume that not all the ice will melt in ice-water mixture) (thermal conductivity o copper 40 W/m.K) A) 7.3 g B) 53 g C). g D).0 g E) 5 g P C = KA T L = 40 8 0 4 00 0.8 = 40. J/S Q = ml 40. 0 60 = m333 0 3 m = 0.075 = 7.5 g = 7.3 g
Term: 6 Sunday, March 9, 07 Page: 8 Q4. For a given mass o an ideal gas what is the ratio T/Ti or the process given in FIGURE 6 A) / B) /4 C) D) 8 E) 4 pv nrt pivi nrti 4 nrt i p V nrt nrt Figure 6 Thereore T T i
Term: 6 Sunday, March 9, 07 Page: 9 Q5. Air that initially occupies 0.40 m 3 at a pressure o 04.0 kpa is expanded isothermally to a pressure o 0.3 kpa and then cooled at constant pressure until it reaches its initial volume. Compute the work done by the air. (Assume air to be an ideal gas). A) 5.6 0 3 J B).5 0 3 J C) 3.40 0 4 J D) 0 E).3 0 4 J P i V i = P V P i P = V V i V = 04 0 3 0.3 0 3 0.40 V = 48 5065 = 0.89m3 W iso = nrtln V V i = P i V i ln ( P i ) = 04 0 3 04 03 0.40 ln ( P 0.3 03) (0.7000) W iso = 999.96 = 9993 J W = P V = 0.3 0 3 (0.89 0.40) = 4378 W = W iso W W net = 5.6 0 3 J
Term: 6 Sunday, March 9, 07 Page: 0 Q6. At a given temperature an ideal gas mixture consists o molecules o types,, and 3, with molecular masses m > m > m3. Rank three types o molecules according to average translational kinetic energy Kavg and rms speed vrms, GREATEST FIRST: A) (Kavg) all tie ; (vrms) 3,, B) (Kavg) all tie ;(vrms),,3 C) (Kavg),,3 ; (vrms),,3 D) (Kavg),,3; (vrms) 3,, E) (Kavg) 3,, ; (vrms) 3,, A ; v r m s = 3RT M ; K avg = 3 K T Q7. A.00 mol sample o a diatomic ideal gas expands adiabatically rom an initial temperature Ti, a pressure o 5.00 atm and a volume o.0 L to a inal volume o 30.0 L. What is the inal temperature o the gas? A) 53 K B) 366K C) 85K D) 45K E) 30K r = C p C v = 7 5 = 7 5 PV = nrt T = PV nr T i (V i ) r = T (V ) r ( P iv i nr ) (V i) r = (T V ) r ( 5.0 05 ( ) 8.3 5 ) = (T 30) 5.0 0 5 ( 8.3 30 ) 5 = T T = 53 K
Term: 6 Sunday, March 9, 07 Page: Q8. 00 g o aluminum at 00 o C is mixed with 50.0 g o water at 0.0 o C, with the mixture thermally insulated. What is the entropy change o the aluminum-water system? (The speciic heat o aluminum is 900 J/kg.K and the speciic heat o water is 4.9 x 0 3 J/kg.K.) A) +.83 J/K B) 0 C) 3.3 J/K D) 9.4 J/K E) +7. J/K 0. 900 (00 T ) = 0.05 490(T 0) 8000 80 T = 09.5 T = 490 8000 + 490 = (09.5 + 80) T T = 56.97 = 57 T = 330 k; s = mcln T T i S sys = S w + S Al S = 0.05 490 ln ( 330 ) + 0. 900 ln (330) = +.83 J /K 93 373 Q9. What is the eiciency o the heat engine shown in FIGURE 7? A) 0.5 B) 0.50 C) 0.0 D) 4.0 E) 0.60 Figure 7 Wout = area under the graph W out (0.)(0000) 000J W 000 out 0.5 Q 4000 in
Term: 6 Sunday, March 9, 07 Page: Q0. 50.0 J o work is done per cycle on a rerigerator with coeicient o perormance o 4.00. How much heat is extracted rom the cold reservoir and exhausted to the hot reservoir per cycle by the rerigerator, respectively? A) 00 J and 50 J B) 00 J and 50 J C) 00 J and 50 J D) 00 J and 50.0 J E) 50.0 J and 00 J W Q H W = 50 J, K = 4.00 K = Q L W 4 = Q L 50 Q L = 00 J Q L Q H = W + Q L = 50 + 00 = 50 J