**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

**Answer:**

#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

**Answer:**

#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

**Answer:**

#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

**Answer:**

#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

**Answer:**

#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

**Answer:**

#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

**Answer:**

#8. The linear coefficient of expansion for copper is** 17 ´
10**^{-6} ^{o}C. A copper disk has a radius of **1.00 cm**
at a temperature of **100 **^{o}C. If its temperature is lowered to
**0 **^{o}C, then the surface of one of its flat faces will decrease by an
amount (**in cm**^{2}) most nearly equal to

**Answer:**

#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/m**^{2}.
The acoustic intensity (**in watt/m**^{2}) at a distance of **5.0
meters** from the speaker is most nearly equal to
**Answer:**

#10. A man carrying a tuning fork that vibrates with frequency **n**
runs at a constant speed **v**_{m} 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
**Answer:**

#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
**Answer:**

#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
**Answer**

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

14. A copper rod has a length of **1.00 meter** and a cross-sectional
area of **0.5 cm**^{2}. 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 **^{o}C. The thermal conductivity of copper is **9.2 ´
10**^{-2} kcal/(sec m** **^{o}C), 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 **^{o}C) inside the furnace is most nearly equal to

**Answer:**

#15. **One gram mole** of a gas has a volume of **11.2 liter** and
is under a pressure of ** 10 atm**. It expands isothermally to a volume of **33.6
liter**. Assuming ideal gas behavior, the work (**in Joules**) done
by the gas is most nearly equal to
**Answer:**