A tuning fork has a frequency of 300 Hz and hence a period of 3.33 103 s. If the tuning fork is in an inertial frame of reference moving by the observer at speed of 0.620 c, what is the frequency of the fork as measured by the observer? (Assume that measurements are strictly by optical means and that the speed of sound waves in air is not pertinent here).
a. 235 Hz
b. 382 Hz
c. 185 Hz
d. 185 Hz
e. 487 Hz
[Ques. 2] Which of the following statements is correct?
a. Because for an object in relative motion is always less than 1, a proper time interval tp is always shorter than the time interval t and a proper length Lp is always longer than the length L.
b. Because for an object in relative motion is always greater than 1, a proper time interval tp is always longer than the time interval t and a proper length Lp is always shorter than the length L.
c. Because for an object in relative motion is always less than 1, a proper time interval tp is always longer than the time interval t and a proper length Lp is always shorter than the length L.
d. Because for an object in relative motion is always greater than 1, a proper time interval tp is always shorter than the time interval t and a proper length Lp is always longer than the length L.
[Ques. 3] A space probe has a 24.7-m length when measured at rest. What length does an observer at rest measure when the probe is going by at a speed of 0.860c?
a. 25.2 m b. 6.43 m
c. 9.19 m d. 12.6 m
[Ques. 4] An astronaut is traveling at a high rate of speed from the Earth to a distant star system. Observers here on Earth note the relativistic effect that the astronaut's clocks run slow. What relativistic effect, if any, does the astronaut observe?
a. Her pulse rate slows.
b. The distance from the Earth to the star system has decreased.
c. Her clocks run faster.
d. There is no relativistic effect to be observed by the astronaut since she is the one doing the moving.
[Ques. 5] A mass is bouncing on the end of a spring with a period T when measured by a ground observer. What would the period of oscillation be (as measured by the same observer) if the mass and spring were moving past the ground observer at a speed of 0.600c?
a. 0.440 T b. 1.25 T
c. 0.600 T d. 1.67 T
[Ques. 6] A spaceship is moving away from an observer at relativistic speed. Its length at rest is 100 m, but the observer measures its length as 60 m. A time interval of 84 s on the spaceship would be measured by the observer to be which of the following?
a. 50.4 s
b. 30.2 s
c. 134 s
d. 140 s
e. 84 s
[Ques. 7] A spaceship of triangular shape, having a length three times its width, is capable of relativistic speeds. How fast would it have to move so that to a stationary observer its length would equal its width?
a. 0.333c
b. 0.816c
c. 0.943c
d. 0.650c
e. This is not possible.
[Ques. 8] Our best measurements from Earth indicate that the star system Alpha Centauri is 4.2 lightyears away. Suppose some of our astronauts traveled there at a speed v = 0.80c. What would the astronauts measure as the distance to Alpha Centauri?
a. 3.1 lightyears
b. 7.0 lightyears
c. 8.8 lightyears
d. 2.5 lightyears
e. 2.7 lightyears
[Ques. 9] If astronauts could travel at v = 0.95c, we on Earth would say it takes (4.2/0.95) = 4.4 years to reach Alpha Centauri, 4.2 lightyears away. The astronauts disagree. How much time passes on the astronaut's clocks?
a. 1.4 years
b. 14.1 years
c. 4.0 years
d. 1.3 years
e. 0.4 years
[Ques. 10] A muon formed high in Earth's atmosphere travels at a speed 0.960c for a distance (as we see it) of 4500 m before it decays. How far does the muon travel as measured in its frame?
a. 2520 m
b. 16,100 m
c. 4320 m
d. 1260 m
e. 4500 m
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