Physics 123
Practice Mid Term Exam
Physics 123 Practice Midterm Exam
Spring 2005
Instructor: John McGill
Earth’s gravitational acceleration: g = 9.8 m/s2
Intensity of 0dB: Io = 10-12 W/m2
Speed of sound in air at room temperature: 343m/s
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Spring 2005
Physics 123
Practice Mid Term Exam
1. What is the maximum value of the acceleration a when x = A cos(ωt + φ )?
a.
b.
c.
d.
e.
2.
Spring 2005
ω
ωt
ω2 A
Aφ
ωA
A simple pendulum on the Earth has a period of one second. What would be its period in s on the moon
where the acceleration due to gravity is 1/6 that of Earth?
a.
b.
c.
d.
e.
6.00
2.45
1.00
0.408
0.167
3. The lowest A on a piano has a frequency of 27.5 Hz. If the tension in the 2.0 meter string is 308 N, and
one-half wavelength occupies the wire, what is the mass of the wire in kg?
a. 0.025
b. 0.051
c. 0.72
d. 0.81
e. 0.37
4. If y = 0.02 sin ((30m-1 )x – (400s -1 )t), the velocity of the wave in m/s is
a. 0.075
b. 13
c. 0.47
d. 2.1
e. 400
5. When standing waves are present on a string of length L the frequency of the third harmonic is
a. v / 2L
b. v / L
c. 3v / 2L
d. 2v / L
e. 5v / 2L
6. Find the frequency in Hz of the second harmonic of a string 1.00 m long. The string, under a tension of 80
−3
N, has a mass per unit length of 2.00 × 10 kg m .
a. 100
b. 200
c. 300
d. 250
e. 150
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Physics 123
Practice Mid Term Exam
Spring 2005
7. A 4.0 kg mass attached to a spring undergoes simple harmonic motion with an angular frequency of
10.0s-1 . What is the frequency, f, of the oscillations?
8. What is the spring constant, k, of the spring in problem 7?
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Physics 123
Practice Mid Term Exam
Spring 2005
9. The wave speed on a 65 cm long guitar string is 428 m/s. What is the lowest resonant frequency of
the string?
10. If the tension in the string in question 9. is 50N, what is the mass per unit length of the string?
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Physics 123
Practice Mid Term Exam
Spring 2005
S2
h=?
S1
3.0 m
Minimum
11. Two sources of sound, S1 and S2, are at two corners of a right triangle as shown. The two sources
vibrate in phase, both at frequency of 400 Hz? The third corner of the right triangle is 3.0 m from
S1 as shown. What is the smallest value of h, the distance between the sources, for which there will
be a minimum at the third corner of the right triangle? (Assume that the speed of sound is 343 m/s).
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Physics 123
Practice Mid Term Exam
Spring 2005
Observer
Source
vs
vo
vo = vs =?
12. A source of sound emits at a frequency of 200 Hz. An observer moves away from the source and
at the same time the source moves away from the observer. The speed of the observer relative to
the air, vo, is the same as the speed of the source relative to the air, vs. (i.e. vo = vs). If the observer
hears a frequency of 184 Hz, what is the speed of the observer and the source? (Assume that the
speed of sound is 343 m/s).
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Physics 123
Practice Mid Term Exam
Spring 2005
Answer Key:
1. c. ω 2 A
2. b. 2.45 s
3 b. 0.051 kg
4. b. 13 m/s
5. c. 3v / 2L
6. b. 200 Hz
7. f = ω/2π = 10.0 s-1/(2(3.14))= 1.59 Hz
8. k = mω2 = (4.0kg)(10.0s-1)2 = 400 N/m
9. f1 = v/2L = 428m/s/(2(0.65m)) = 330 Hz
10. µ = τ/v 2 = 50N/(428m/s)2 = 2.7x10-4 kg/m
11. h = (r1 + v / 2 f ) 2 − r12 = (3.0m + (343m / s )/2(400s − 1))2 − (3.0m) 2 = 1.7m
12. vo = vs = v(f-f')/(f+f') = (343m/s)(200Hz-184Hz)/(200Hz+184Hz) = 14.3 m/s
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