Exam Review #3 Simple
Harmonic Motion through
Entropy
Supplemental Instruction
Iowa State University
Leader: Wesley
Course: PHYS 221
Instructor: Whisnant
Date: 05/04/2014
Practice Exam #3
Please bring this with you to the SI review
session on Sunday, May 4th. It will behoove
you NOT to look past this page until then.
(You SHOULD look at the last three pages
though.)
1060 Hixson-Lied Student Success Center  515-294-6624  sistaff@iastate.edu  http://www.si.iastate.edu
Do NOT plug in numbers until you have solved for the desired variable!
Try to solve each problem algebraically first.
1. Water near the surface of the ocean has a temperature of 25° C. Water 1500 m below the
surface has a temperature of 2° C. What is the maximum efficiency of a heat engine
which uses the warm water as a hot reservoir and the cool water as a cold reservoir?
A. 6.0%
B. 7.7%
C. 23%
D. 51%
E. 63%
F. I don’t know
2. The average speed of a molecule in a particular sample of an ideal monatomic gas is 540
m/s. If the gas is in a 1.50-m3 container at STP, what is the total mass, in kg?
A. 1.19
B. 1.33
C. 2.04
D. 3.26
E. 4.78
F. I don’t know
Do NOT plug in numbers until you have solved for the desired variable!
Try to solve each problem algebraically first.
3. For the pV diagram shown, what is the work
done by the gas for one cycle (abca), in L-atm?
Process bc is adiabatic, and you may assume that
γ = 1.40.
A.
B.
C.
D.
E.
F.
-0.25
-0.16
0.16
0.25
0.33
I don’t know
4. When an ideal gas is allowed to expand isothermally from volume V1 to a larger volume
V2, the gas does an amount of work equal to W12.
If the same ideal gas is allowed to expand isobarically from volume V1 to V2, the gas does
an amount of work that is:
A.
B.
C.
D.
E.
F.
Greater than W12
Equal to W12
Less than W12
Either A, B, or C, depending on the ratio V2/V1
Either A, B, or C, depending on the final temperature
42
Do NOT plug in numbers until you have solved for the desired variable!
Try to solve each problem algebraically first.
5. You have 2.00 mol of an ideal diatomic gas and 2.00 mol of an ideal gas which has a
total of 7 degrees of freedom (rotational and translational). The gases are in identical
fixed containers and initially both gases are at the same temperature. If the same amount
of heat flows into each gas, which gas will undergo the greatest increase in temperature?
A.
B.
C.
D.
E.
F.
They have the same increase in temperature
The diatomic gas
The gas with 7 degrees of freedom
The answer depends on the molar mass of the gases
The answer depends on the value of the initial temperature
43?
(Extra Practice: How many degrees of freedom does a diatomic gas have? How many does a
monatomic gas have?)
6. A siren is moving towards an observer and emitting a sound at a frequency of 5000 Hz
and a wavelength of 0.498 m. The observer is stationary, and hears a frequency f and will
measure a wavelength λ for the sound such that:
A. f > 5000 Hz and λ > 0.498 m
B. f > 5000 Hz and λ < 0.498 m
C. f > 5000 Hz and λ = 0.498 m
D. f = 5000 Hz and λ > 0.498 m
E. f = 5000 Hz and λ < 0.498 m
F. Nope. Definitely 42.
Do NOT plug in numbers until you have solved for the desired variable!
Try to solve each problem algebraically first.
7. The side S of a cube is measured with an ordinary plastic ruler. The result, along with the
estimated uncertainty, is 𝑆 = (30.0 ± 0.6) mm. Which of the following is the volume
of the cube with the corresponding propagated uncertainty, in mm?
A.
B.
C.
D.
E.
F.
27000 ± 0.6
27000 ± 1.8
27000 ± 16.2
27000 ± 270
27000 ± 1620
I don’t know
8. A balloon is filled with air at room temperature and is tied tightly. The balloon is then
slowly cooled down by holding it in an ice cold bath. Both the temperature and volume
(via water displacement) are measured throughout the process. Which of the following
graphs is closest to the graph you will obtain with that data?
Do NOT plug in numbers until you have solved for the desired variable!
Try to solve each problem algebraically first.
9. You have just come into warm house of your friend, Throckmorton, from the cold. To
greet him, you immediately place your hand of temperature 0 °C on his cheek, which is a
temperature of 30 °C. Throckmorton is silly enough to let you keep your hand there until
your hand and his cheek reach thermal equilibrium at 15 °C. You can assume that the
effective mass of both your hand and his cheek are 0.5 kg, the effective specific heat of
human flesh is 3470 J/kg-K, and you can assume that heat only flows between your hand
and his cheek. What is the change in entropy for this system?
A.
B.
C.
D.
E.
F.
-88.1 J/K
-4.71 J/K
0.00 J/K
4.71 J/K
92.8 J/K
Throckmorton is silly. It’s no fun if he doesn’t squirm.
END OF “TEST.” THE QUESTIONS AFTER THIS ARE ALL ADDITIONAL PRACTICE.
Do NOT plug in numbers until you have solved for the desired variable!
Try to solve each problem algebraically first.
1. There is a two stringed instrument shown in the figure below, and its metal strings are
35.0 cm long. Both strings are under the same tension. String 1 has a mass of 8.00 g, and
produces a frequency of 262 Hz (middle C) in its fundamental mode.
a. What is the tension in this string?
b. What is the mass of sting 2 so that it produces a fundamental frequency of 466 Hz
(A#)?
c. To extend the range of the instrument, there is a fret included just under the
strings but not normally touching them (like a guitar). How far from the upper end
should this fret be located so that when you press string 1 tightly against it, this
string will produce a frequency of 277 Hz (C#) as its fundamental frequency?
2. A uniform 165-N bar is supported horizontally by two identical wires A and B. A small
185-N cube of lead is placed ¾ of the way from A to B. The wires are each 75.0 cm long
and have a mass of 5.50 g. If both of them are simultaneously plucked at the center, what
is the frequency of the beats that they will produce when vibrating in their fundamental?
(Hint: Draw a Free Body Diagram.)
Do NOT plug in numbers until you have solved for the desired variable!
Try to solve each problem algebraically first.
3. Two identical loudspeakers (same wave amplitude, frequency, speed, and wavelength)
are 2.00 m apart at points A and B. The waves produced by the speakers have a
frequency of 784 Hz. The speed of sound in air is 344 m/s. A small microphone is moved
out from point B to point C along a line perpendicular to the line connecting A and B.
a. At what distances x from B will there be constructive interference?
b. At what distances x from B will there be destructive interference?
c. If the frequency is low enough, there will be no positions of along BC at which
destructive interference occurs. What is the cut-off frequency for this to be the
case?
Two loudspeakers A and B, are driven by the same amplifier and emit sinusoidal waves
in phase. The frequency of the waves emitted by heach speaker is 172 Hz. You are 8.00
m from A. What is the closest you can be to B and be at a point of destructive
interference?
Do NOT plug in numbers until you have solved for the desired variable!
Try to solve each problem algebraically first.
Quick notes:
-
The first overtone of a standing wave is its second harmonic. (its second overtone is
its 3rd harmonic, and so forth)
-
In a standing wave, a wavelength contains 3 nodes, and 2 anti-nodes. (see picture
below)
-
A pressure node is a displacement anti-node, and a pressure anti-node is a
displacement node. In most cases, nodes and anti-nodes refer to displacement nodes.