1. A basic postulate of Einstein's theory of relativity is:
A.moving clocks run more slowly than when they are at rest
B.moving rods are shorter than when they are at rest
C.light has both wave and particle properties
D.the laws of physics must be the same for observers moving with uniform velocity relative to each other
E.everything is relative


2. Two events occur simultaneously at separated points on the y axis of reference frame S. According to an observer moving in the positive x direction:
A.the event with the greater y coordinate occurs first
B.the event with the greater y coordinate occurs last
C.either event might occur first, depending on the observer's speed
D.the events are simultaneous
E.none of the above


3. Two events occur on the x axis separated in time by Dt and in space by Dx. A reference frame, traveling at less than the speed of light, in which the two events occur at the same time:
A.exists no matter what the values of Dx and Dt
B.exists only if Dx/Dt < c
C.exists only if Dx/Dt > c
D.exists only if Dx/Dt = c
E.does not exist under any condition


4. Two independent events occur 100 m apart with an intervening time interval of 0.42 ms. The proper time in ms between the events is:
A.0
B.0.16
C.0.26
D.0.42
E.0.69


5. A rocket traveling with constant velocity makes a 8.4 × 1015 m trip in 1 year. The proper time in years between events which mark the beginning and end of the trip is:
A.0.21
B.0.46
C.1.0
D.2.2
E.4.7


6. A meson when at rest decays 2 ms after it is created. If moving in the laboratory at 0.99c, its lifetime according to laboratory clocks would be:
A.the same
B.0.28 s
C.14 ms
D.4.6 s
E.none of these


7. Relative to reference frame 1, reference frame 2 moves with speed v in the negative x direction. When the origins of the two frames coincide the clocks in both frames are set to zero. An event occurs at coordinate x1 and time t1 as measured in reference frame 1 and at coordinate x2 and time t2 as measured in frame 2. If , then the coordinates and times of the event are related by:
A.x2 = g [x1 – vt1] and t2 = g [t1 – vx1 / c2]
B.x2 = g [x1 – vt1] and t2 = g [t1 + vx1 / c2]
C.x2 = g [x1 + vt1] and t2 = g [t1 – vx1 / c2]
D.x2 = g [x1 + vt1] and t2 = g [t1 + vx1 / c2]
E.none of the above are correct


8. Observer A measures the velocity of a rocket as ² and a comet as 7. Here 7 and ² are parallel and in the direction of the observer's positive x axis. The speed of the comet as measured by an observer on the rocket is:
A.(u – v)/(1 – uv/c2)
B.(u – v)/(1 – v2/c2)
C.(u – v)/(1 – v2/c2)1/2
D.(u – v)/(1 + uv/c2)
E.(u + v)/(1 – uv/c2)


9. Light from some stars shows an apparent change in frequency because of:
A.interference
B.refraction by layers of air
C.diffraction
D.reflection
E.relative motion


10.

While emitting light of proper frequency f0, a source moves to the right with speed c/4 relative to reference frame S. A detector, to the left of the source, measures the frequency to be f, which is greater than f0. This means:




A.the detector is moving to the right with a speed that is greater than c/4 relative to S
B.the detector is moving to the right with a speed that is less than c/4 relative to S
C.the detector is moving to the left with a speed that is greater than c/4 relative to S
D.the detector is moving to the left with a speed that is less than c/4 relative to S
E.the detector is not moving


11. A source at rest emits light of wavelength 500 nm. When it is moving at 0.90c away from an observer, the observer detects light of wavelength:
A.26 nm
B.115 nm
C.500 nm
D.2200 nm
E.9500 nm


12. A particle with rest mass m moves with speed 0.6c. Its kinetic energy is:
A.0.18mc2
B.0.22mc2
C.0.25mc2
D.mc2
E.1.25mc2


13. The velocity of an electron is changed from c/2 in the –x direction to c/2 in the +x direction. As a result, its kinetic energy changes by:
A.mc2
B.0.5mc2
C.
D.2mc2
E.zero


14. The work that must be done to increase the speed of an electron (m = 9.11 × 10–31 kg) from 0.90c to 0.95c is:
A.2.6 × 10–13 J
B.8.2 × 10–13 J
C.3.2 × 10–13 J
D.7.4 × 10–14 J
E.3.8 × 10–15 J


15. An electron (m = 9.11 × 10–31 kg) has a speed of 0.95c. Its momentum is:
A.2.6 × 10–22 kg × m/s
B.2.9 × 10–22 kg × m/s
C.6.0 × 10–22 kg × m/s
D.8.3 × 10–22 kg × m/s
E.8.8 × 10–22 kg × m/s


16. The mass of a particle is m. In order for its total energy to be twice its rest energy, its momentum must be:
A.mc/2
B.
C.mc
D.
E.2mc


17. If the kinetic energy of a particle is equal to its rest energy then its speed must be:
A.0.25c
B.0.50c
C.0.87c
D.c
E.unknown unless its mass is given


18. If the mass of a particle is zero its speed must be:
A.c
B.infinite
C.0
D.any speed less than c
E.any speed greater than c


19. A particle with zero mass and energy E carries momentum:
A.Ec
B.Ec2
C.
D.E/c
E.E/c2


20. The magnitude of the momentum of a particle can never exceed:
A.mc, where m is its mass
B.E/c, where E is its energy
C.K/c, where K is its kinetic energy
D.none of the above, but there is an upper limit
E.none of the above; there is no upper limit


21. The speed of a sound wave is determined by:
A.its amplitude
B.its intensity
C.its pitch
D.number of overtones present
E.the transmitting medium


22. Take the speed of sound to be 340 m/s. A thunder clap is heard about 3 s after the lightning is seen. The source of both light and sound is:
A.moving overhead faster than the speed of sound
B.emitting a much higher frequency than is heard
C.emitting a much lower frequency than is heard
D.about 1000 m away
E.much more than 1000 m away


23. A sound wave has a wavelength of 3.0 m. The distance from a compression center to the adjacent rarefaction center is:
A.0.75 m
B.1.5 m
C.3.0 m
D.need to know wave speed
E.need to know frequency


24. A plane produces a sonic boom only when:
A.it breaks the sound barrier
B.it emits sound waves of high frequency
C.it flys at high altitudes
D.it flys on a curved path
E.it flys faster than the speed of sound


25.

The Doppler shift formula for the frequency detected is



where f' is the frequency emitted, v is the speed of sound, vD is the speed of the detector, and vs is the speed of the source. Suppose the source is traveling at 5 m/s away from the detector, the detector is traveling at 7 m/s toward the source, and there is a 3 m/s wind blowing from the source toward the detector. The values that should be substituted into the Doppler shift equation are:


A.vD = 7 m/s and vs = 5 m/s
B.vD = 10 m/s and vs = 8 m/s
C.vD = 4 m/s and vs = 2 m/s
D.vD = 10 m/s and vs = 2 m/s
E.vD = 4 m/s and vs = 8 m/s


26. The rise in pitch of an approaching siren is an apparent increase in its:
A.speed
B.amplitude
C.frequency
D.wavelength
E.number of overtones


27.

Two small identical speakers are connected (in phase) to the same source. The speakers are 3 m apart and at ear level. An observer stands at X, 4 m in front of one speaker as shown. The sound he hears will be least intense if the wavelength is:




A.1 m
B.2 m
C.3 m
D.4 m
E.5 m


28. An organ pipe with both ends open is 0.85 m long. Assuming that the speed of sound is 340 m/s, the frequency of the third harmonic of this pipe is:
A.200 Hz
B.300 Hz
C.400 Hz
D.600 Hz
E.none of these


29.

Organ pipe Y (open at both ends) is twice as long as organ pipe X (open at one end) as shown. The ratio of their fundamental frequencies fX:fY is:




A.1:1
B.1:2
C.2:1
D.1:4
E.4:1


30. An organ pipe with one end closed and the other open has length L. Its fundamental frequency is proportional to:
A.L
B.1/L
C.1/L2
D.L2
E.


31. A vibrating tuning fork is held over a water column with one end closed and the other open. As the water level is allowed to fall, a loud sound is heard for water levels separated by 17 cm. If the speed of sound in air is 340 m/s, the frequency of the tuning fork is:
A.500 Hz
B.1000 Hz
C.2000 Hz
D.5780 Hz
E.578,000 Hz


32.

A stretched wire of length 1.0 m is clamped at both ends. It is plucked at its center as shown. The three longest wavelengths in the wire are (in meters):




A.4, 2, 1
B.2, 1, 0.5
C.2, 0.67, 0.4
D.1, 0.5, 0.33
E.1, 0.67, 0.5


33. A piano wire has a length of 81 cm and a mass of 2.0 g. If its fundamental frequency is to be 394 Hz, it must be stretched by a tension of:
A.0.32 N
B.63 N
C.130 N
D.250 N
E.none of these


34. If the length of a piano wire (of given density) is increased by 5%, what approximate change in tension is necessary to keep its fundamental frequency unchanged?
A.decrease of 10%
B.decrease of 5%
C.increase of 5%
D.increase of 10%
E.increase of 20%


35. If the power output of a sound source emitting spherical waves is 100 W, the sound intensity 5.0 m from the source is:
A.0.32 W/m2
B.1.6 W/m2
C.4.0 W/m2
D.20 W/m2
E.100 W/m2


36. Two notes are an "octave" apart. The ratio of their frequencies is:
A.8
B.10
C.
D.2
E.


37. To produce beats it is necessary to use two waves:
A.traveling in opposite directions
B.of slightly different frequencies
C.of equal wavelengths
D.of equal amplitudes
E.whose ratio of frequencies is an integer



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