Third Examination
Physics 104
03 May 1977

#1.  A constant volume gas thermometer shows a pressure of 25.0 cm of mercury when held at the triple point temperature of water.  The gas thermometer is then immersed in a mixture of the solid and liquid phases of a pure substance in thermal equilibrium, and after attaining equilibrium the thermometer shows a pressure of 30.0 cm of mercury (its volume having been kept constant).  The temperature (in degrees Celsius) of the mixture is most nearly equal to

a) 55     b) 273    c) 328     d) 228     e) -45

#2.  A closed organ pipe has a length of 1 meter. The wavelength (in meters) of its third harmonic (second overtone) is most nearly equal to

a) 1/3     b)3/4     c) 1.0     d) 4/5     e) 1/2

#3. Gas in a chamber is taken through the cycle shown in the sketch.  Along the path ABC, Q = 100 cal and W = 50 cal.  However, along the path ADC, W = 25 cal.  Along the path CDA, the value of Q (in cal) is most nearly equal to

a) 0      b) 25      c) 125      d) -75      e) 50

#4.   A string having a mass of  0.05 kg and a length of 2.00 meters is stretched along the x-axis under a tension of 10.0 Newtons.  If y is vertical displacement of points along the string at time t, then a correct partial differential equation for the (undamped) wave motion of the spring is

a) 2y/x2 + 20 m/s y/t = 0
b) 2y/x2 - s2/400 m2 2y/t2 = 0
c) 2y/x2 + 20 m/s 2y/t2 = 0
d) y/x - s2/400 m2 2y/t2 = 0
e) 2y/x2 + s/20 m 2y/t2 = 0

#5.  A speaker on a rocket emits sound at a frequency of 1000 cycles/sec (Hz), while moving directly away from you at a speed of 100 m/sec.  The speed of sound is 330 m/sec.  The frequency (in cycles/sec) of the sound you actually hear is most nearly equal to

a) 1000       b)697            c) 767            d) 1303            e)  1.435

#6.  Two waves of equal amplitudes and wavelengths travel in opposite directions along a stretched string, setting up the pattern shown in the sketch.  The time for point A on the string to move down to position B is 0.10 sec.  The equation for one of the waves is

a) y = (0.10 m) ´ sin(2.0 x/m + 0.010t/s)
b) y = (0.05 m) ´ sin(3x/(2m) - 0.020t/s)
c) y = (0.10 m) ´ sin(2.0 x/m) cos(0.010t/s)
d) y = (0.05 m) ´ sin(3px/(2m) + 0.020pt/s)
e) y = (0.05 m) ´ sin(2px/m - 100pt/s)

#7. An aluminum rod is 1.00 meters long.  It is held vertically at a point 1/4 of its length from the upper end and is struck a blow on that end with a hammer so that it "rings" -- producing a sound of a given pitch.  If the speed of the longitudinal sound wave in aluminum is 5100 m/sec, the frequency (in cycle/sec) of the loudest sound we hear is most nearly equal to
a) 5100   b) -2550   c) 10200    d) -6800      e) +1275

#8. The linear coefficient of expansion for copper is 17 ´ 10-6 oC. A copper disk has a radius of 1.00 cm at a temperature of 100 oC. If its temperature is lowered to 0 oC, then the surface of one of its flat faces will decrease by an amount (in cm2) most nearly equal to
a) 0.011     b) 5.3 ´ 10-3     c) 3.4 ´ 10-3     d) 1.7 ´ 10-3    e) 2.7 ´ 10-3

#9. A hi-fi engineer has designed a speaker that is spherical in shape and emits sound isotropically.  for a certain continuous sound the acoustic intensity 6.0 meters from the speaker is 0.0376 watt/m2.  The acoustic intensity  (in watt/m2) at a distance of 5.0 meters from the speaker is  most nearly equal to

a) 0.0261    b) 0.0376    c) 0.0313  d) 0.0451  e) 0.0541

#10. A man carrying a tuning fork that vibrates with frequency n runs at a constant speed vm toward a wall.  The air is still.  A listener standing some distance directly behind the runner hears a beat frequency.  The speed of sound in air is v.  The beat frequency the listener hears  is most nearly equal to

a) 2n vm/v    b) 2n v/(v-vm c) nv [1/(v+vm)- 1/(v+vm)]  d)  n (v+vm)/v   e) 2n v/vm

#11. A plane flies with 5/4 the speed of sound.  The sonic boom reaches a man on the ground exactly one minute after the plane passed directly overhead.  The speed of sound in air is 330 m/sec. The altitude of the plane (in meters) is most nearly equal to

a) 11,880    b) 19,880    c) 33,000   d) 24,750   e) 15,840

#12. Consider 1.00 gram-moles of nitrogen gas (molecular weight = 28 a.m.u) under standard conditions of temperature  and pressure (STP).  The root-mean-square speed (in meters/sec) of the nitrogen molecules is most nearly equal to

a) 493     b) 1.5        c) 3.1       d)5.3        e) 318

#13. The heat of fusion of ice is 80 cal/gm.  Ice at 0 oC is to be mixed with 200 gm of an alcohol-water solution (specific heat = 0.95 cal/(gm oC) at an initial temperature of 25 oC.  In order that the final temperature of the mixture should be 41 oFahrenheit, the mass (in grams) of ice should be most nearly equal to

a) 150          b) 45          c) 32       d) 38     e) 190

14. A copper rod has a length of  1.00 meter and a cross-sectional area of 0.5 cm2.  One end is held inside a furnace at an unknown temperature, while the other end is placed in a mixture of ice-and-water at 0 oC.  The thermal conductivity of copper is 9.2 ´ 10-2 kcal/(sec m oC), and the heat of fusion of ice is 80 cal/gm.  Under steady-state conditions, it is found that 10.0 gm of ice is melted every 5.0 minutes.  The temperature (in oC) inside the furnace is most nearly equal to