Physics 2306
Fall 2007
First Exam
FORM A
1) The displacement of air molecules in a sound wave is given by
s(x,t) = (0.20 cm) sin[(10
π
radians/meter) x] sin[(3000
π
radians/second) t]
Which one of the following statements is true?
A.
The wave is a transverse wave and the displacement of air molecules and the
pressure fluctuation are in phase.
B.
The wave is a transverse wave and the displacement of air molecules and the
pressure fluctuation are 90
°
out of phase.
C.
The wave moves in the xdirection with a speed equal to 300 m/s.
D.
The wave is a transverse wave
and the displacement of air
molecules and the pressure
fluctuation are 180
°
out of phase.
E.
The wave has an antinode at x
= 0.25 meters.
F.
The wave is a longitudinal wave
and the displacement of air
molecules and the pressure fluctuation are in phase.
G.
The wave is a longitudinal wave and the displacement of air molecules and the
pressure fluctuation are 180 degrees out of phase.
H.
The wave has a node at time equal to 0.0010 seconds.
25) The displacement of a string from equilibrium is given by
y(x,t) = (0.030 m)cos[(4.0
π
rad/meter)x + (1600
π
rad/sec)t]
2) What is the amplitude (in meters) of the wave?
sin[(10
π
radians/meter) x] is one for x = 0.25
meters which implies that the amplitude of the
displacement is maximum at that position
which implies an antinode at that position.
General expression for a traveling wave is
y(x,t) = A cos[ kx
±
ω
t]
where A is the amplitude, k = 2
π
/
λ
is the wave number, and
ω
= 2
π
f =
2
π
/T.
Comparing the specific example given above to the general
expression, you see that
A = 0.030 m
k = 4.0
π
ω
= 1600
π
and that the wave is moving in the negative xdirection since there is a plus
sign between kx and
ω
t.
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3) What is the period (in seconds) of the wave?
4) What is the wavelength (in meters) of the wave?
5) What is the velocity of propagation (in meters/second) of the wave (positive wave
velocity is in the +xdirection and negative wave velocity is in the
−
xdirection)?
A.
6400
B.
−
6400
C.
4.0
D.
−
4.0
E.
1600
F.
−
1600
G.
400
H.
−
400
6) A pipe is open at one end.
The frequency of sound from this pipe is 344 Hz?
If this
normal mode is the third harmonic, what is the length of the pipe (in meters)?
Assume
the speed of sound is 344 m/s.
T = 2
π
/
ω
= 2
π
/1600
π
λ
= 2
π
/k = 2
π
/4.0
π
The wave relation is
ω
= v k
where v is the speed of the wave.
Therefore
v =
ω
/k =1600
π
/4.0
π
= 400 m/s
The velocity is in the negative xdirection for the reason
given in question 2.
The length of a pipe that is open at one end is
λ
/4 for the first
harmonic.
The frequency of the first harmonic is
f
1
= v/
λ
= v/4L
where L is the length of the pipe.
The next harmonic occurs
when the length of the pipe is equal to
λ
/4 +
λ
/2 = 3
λ
/4.
The
frequency of this harmonic is
f = v/
λ
= 3v/4L = 3f
1
So there is no second harmonic and the length of the pipe is
L = 3
λ
/4 = 3 v/4 f
since
λ
f = v.
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 Fall '06
 YKim
 Physics, Fundamental physics concepts, A. B. C. D. E. F. G.

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