Physics 101
Classical Physics
Spring 2010
Homework 11 Solutions
DUE IN CLASS ON April 27
1. The speed of sound wave is determined by:
(a) its amplitude (b) its intensity (c) its path (d) number of harmonics present
(e) the transmitting medium
The speed sound is the speed at which small density fluctuations travel through a medium
which depends only on the transmitting medium, not the characteristics of the wave itself.
2. Which string on a guitar is likely to have the lowest pitch?
(a) The thinnest, tightest string
(b) The thinnest, loosest string
(c) The thickest, tightest string
(d) The thickest, loosest string
(e) They all have the same pitch
The speed waves travel on a string is
v
=
p
T/μ
where
T
is the tension in the string and
μ
is the mass per unit length. So, waves will travel slowest on a string with small tension and
large mass per unit length. This corresponds to the thickest, loosest string. The frequency
of the waves on the string is equal to the product of the wavelength and propagation speed,
so the string with the slowest wave propagation speed will have the lowest pitch.
3. Suppose object C is in thermal equilibrium with both object A and object B.
The zeroth law of thermodynamics tells us:
(a) that C will always be in equilibrium with A and B, no matter what happens
(b) that C must transfer energy to both A and B
(c) that A is in thermal equilibrium with B
(d) that A cannot be in thermal equilibrium with B
(e) nothing about the relationship of A and B
4. Two identical rooms in a house are connected by a doorway. The temperatures
in the two rooms are maintained at different values. Which room contains more
air ? (a) the room with higher temperature
(b) the room with lower temperature
(c) the room with higher pressure
(d) neither because both have the same pressure
(e) neither because both have the same volume
With the pressure and volume the same in each room, the ideal gas law states that
n
1
T
1
=
n
2
T
2
where
T
1
and
T
2
are the temperatures in the 2 rooms and
n
1
and
n
2
are the amount
of gas in the 2 rooms. If
T
1
> T
2
, then this implies
n
1
< n
2
. Therefore, the room with the
lower temperature contains more gas.
1
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5. The temperature of a gas is most closely related to: (a) the bonding energy of
its molecules
(b) its total molecular kinetic energy
(c) the sizes of its molecules
(d) the potential energy of its molecules
(e) the total number of molecules
6. Two waves in one string are described by
y
1
=
A
1
cos(
k
1
x

ω
1
t
)
y
2
=
A
2
cos(
k
2
x

ω
2
t
)
where
A
1
= 3
.
3
cm,
A
2
= 4
.
4
cm,
k
1
= 4
rad/cm,
k
2
=5 rad/cm,
ω
1
= 5
rad/s and
ω
2
= 2
rad/sec. Use cm for both
y
and
x
.
(a) Find the superposition of the waves
y
1
+
y
2
at the position
x
1
= 1
cm and the
time
t
1
= 1
s. Answer in units of cm.
At
x
1
and
t
1
, the component waves give
y
1
(
x
1
, t
1
)
=
A
1
cos(
k
1
x
1

ω
1
t
1
) = (3
.
3 cm) cos(4

5) = 1
.
78 cm
y
2
(
x
1
, t
1
)
=
A
2
cos(
k
2
x
1

ω
2
t
1
) = (4
.
4 cm) cos(5

2) =

4
.
36 cm
The superposition is then
y
1
(
x
1
, t
2
) +
y
2
(
x
1
, t
1
) =

2
.
58 cm
(b) Find the superposition of the waves
y
1
+
y
2
at the position
x
2
= 1
cm and
time
t
2
= 0
.
5
s. Answer in units of cm.
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 Physics, Thermodynamics, Work, 2.88 cm, 3.48 cm

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