Physics 107: Ideas of Modern Physics

Transcription

1 Physics 107: Ideas of Modern Physics Exam 2 March 14, 2007 Name SOLUTIONS ID # Section # On the Scantron sheet, 1) Fill in your name 2) Fill in your student ID # (not your social security #) 3) Fill in your section # (under ABC of special codes) Useful constants: c= speed of light = 3x10 8 m/s sound speed in air = 340 m/s k = electric constant = 9x10 9 Nm 2 /C 2 g= accel. of gravity on Earth = 10 m/s 2 G= gravitational constant = 6.7x10-11 N-m 2 /kg 2

2 1. a 2 2. A 1020 Hz tone is generated by a speaker. What is the wavelength of the sound wave? a m b. 3.0 m c. 1.0 m d m e m This is a sound wave, so it travels at 340 m/s. The wavelength is determined from the frequency as λ=v/f = (340 m/s)/1020 Hz = 0.33 m. 3. An example of a longitudinal wave is a. a water wave. b. a sound wave. c. an electromagnetic wave. d. a wave on a rope. e. a frequency wave. A sound wave compresses the air in the direction in which the wave is moving. This is a longitudinal wave. 4. Two wave pulses on a rope approach each other as shown to the right. Some time later, the rope looks like: A. B. C. D. E. 5. In your room you have two speakers in different corners. At your desk you used to be exactly 1 meter from each, so that there is no interference. But now your roommate moved one of your speakers 0.2 m further away from your desk. At what frequency will you hear destructive interference? a Hz b Hz c. 850 Hz d. 680 Hz e. 136 Hz Destructive interference occurs when the crest of a wave from one speaker lines up with the trough of the wave from the other. Since in the first configuration, the crests lined up to produce no destructive interference, the extra 0.2m must be half of one wavelength. Then a whole wavelength is 0.4m. The frequency corresponding to that wavelength is f = v/λ=(340 m/s) / 0.4 m = 850 Hz 2

3 3 6. A car blowing its horn drives directly towards me at constant velocity, then passes and drives directly away from me at the same constant velocity. I hear a. A constant pitch as the car approaches, and a lower constant pitch after the car has passed me. b. A pitch rising in time as the car approaches, and a pitch falling in time after the car has passed. c. A constant pitch as the car approaches, and a higher constant pitch after the car has passed me. d. A pitch falling in time as the car approaches, and a pitch rising in time after the car has passed. e. A constant pitch as the car approaches, and a pitch falling in time after the car has passed. 7. Your Badger radio network broadcasts on AM This frequency is 1,310 khz (1 khz = 1000 Hz). What is the wavelength of this wave? a. 75 meters b. 385 meters c. 2.3 meters d. 230 meters e meters This is an electromagnetic wave, which travels at the speed of light c=3x10 8 m/s. The frequency is 1,310,000 Hz. The wavelength is then λ=c/f =( 3x10 8 m/s ) / 1.31x10 6 Hz =229 m. Quite long! 8. An observed source of magnetic fields is: a. magnetic monopoles b. magnetic currents c. electric charges d. voltage currents e. electric currents 9. The force between two electrically charged particles 0.4 m apart is found to be attractive, with magnitude 2x10-10 N. What is the force when the separation is increased to 0.8 m? a. 4.0x10-10 N, attractive. b. 4.0x10-10 N, repulsive c. 8.0x10-10 N, repulsive d. 0.5x10-10 N, attractive. e. 1.0x10-10 N, repulsive The separation doubles, and the force decreases with the square of the separation, so the force decreases by a factor of 4. 3

4 4 10. Complete destructive interference of two waves occurs when a. crests of both waves line up with each other b. troughs of both waves line up with each other c. crests of one wave line up with troughs of other d. crests of one wave alternate with troughs of other e. the two waves have only crests 11.Your microwave oven beams electromagnetic radiation at the food inside, and the food warms by absorbing the radiation. To increase the efficiency, the oven is approximately a resonant cavity, with one wavelength of microwave radiation fitting inside the length. If the oven has a length of 15 cm (0.15 m), find the operating frequency. (1 Giga-Hertz=10 9 Hz) a. 2.0 Giga-Hertz b. 1.0 Giga-Hertz c. 0.1 Giga-Hertz d. 0.2 Giga-Hertz e. 20 Giga-Hertz One wavelength fits into 0.15 m, so the wavelength of the radiation is 0.15 m. The frequency is f=c/λ = (3x10 8 m/s) / 0.15 m = 2x10 9 Hz = 2 GHz. 12. An electron moves continuously up and down in one corner of room. An experimenter in the opposite corner of the room finds out that in his corner there is a. an electromagnetic wave. b. an unchanging electric field. c. an unchanging magnetic field. d. a charge. e. a current. 13. The first transatlantic radio broadcast was made in 1895 from Cornwall, England and detected in St. John s, Newfoundland, a distance of 2,100 miles (3,400 km, 1 km=1000 m). To cover this distance, it took the radio signal a seconds b seconds c seconds d. 3.2 seconds e. 88 seconds The propagation speed is the speed of light c = 3x10 8 m/s. The travel time is than 3,400,000 m / 3x10 8 m/s = sec. 4

5 14. Einstein s special theory of relativity is valid in inertial reference frames. An inertial reference frame is defined to be one that 5 a. is stationary. b. moves as constant speed. c. moves at constant velocity. d. moves at constant acceleration. e. shows no gravitational force. 15.One space ship is catching up to and passing another on the same trip between two stars. The passing ship moves at 0.9c and the other ship at 0.45c. The passing ship flashes its headlights before passing. An observer on the slower ship measures the light from the headlights to be moving at what speed relative to the slower ship? a. 1.0c b. 0.45c c. 0.0c d. 1.45c e. 1.67c A basic premise of special relativity is that electromagnetic radiation propagates at the same speed c in all reference frames. 16. A man on a fast motorcycle moving at 0.5c relative to an observer on the ground throws a baseball forwards in the motorcycle reference frame. Who measures the proper time interval between the ball being thrown, and passing the front wheel of the motorcycle 1 meter away? a. The motorcycle rider b. The ground observer c. Both d. Neither e. Depends on speed of ball The proper time is observed in the frame where the two events occur at the same spatial location. This is not the case for either of these observers. 17. An astronaut travels by the Earth at 0.6c. Someone stationary on Earth holds a meter stick. The astronaut measures the length of this meter stick to be. a. Less than one meter. b. More than one meter. c. Exactly one meter. d. Need to know Earth velocity. e. Depends on Earth reference frame. The proper length is measured in the frame at rest with respect to the meter stick. This is the Earth frame. The length measured in any other frame is shorter. This is length contraction. 5

6 6 18. An astronaut moves at a constant velocity of 0.5c relative to a person on Earth. The astronaut watches the Earth observer through a telescope and sees that a. the earthling ages more slowly b. the earthling ages more quickly. c. the earthling ages at the same rate. d. aging depends on whether velocity is positive or negative. e. the earthling has brown eyes The earthling measures the proper time for their own aging process, and any other time interval measured is longer (time dilation). So the astronaut measures a time longer than one second for each second that has ticked on the earthlings. This means the astronaut observes the earthling to age more slowly. 19. An astronaut in a spaceship moves relative to an Earth observer. The Earth observer measures the time interval between heart beats of the astronaut. As the speed of the astronaut gets closer and closer to the speed of light (assume the astronaut does not get excited!), the earth observer sees that the time interval between the astronaut s heart beats a. increases without bound b. decreases, getting arbitrarily close to zero. c. increases, but never exceeds c, the speed of light. d. decreases, approaching c/10. e. increases for positive speeds, decreases for negative speeds. The time dilation effect is proportional to γ, which increases without bound as the speed approaches the speed of light. 20. An average person requires 3000 Calories of energy per day, usually ingested as food. This is 1.25x10 7 Joules. So the entire population of the Earth (~6.5 billion people) requires about 9x10 16 Joules of energy per day. If this could be provided by mass energy, how much mass per day would be required? a. 0.3 gm b. 0.5 gm c. 30 gm d. 0.3 kg e. 1 kg Required energy is 9x10 16 J. If this comes from mass energy, then E=mc 2, m=c 2 /E = (3x10 8 m/s) 2 /9x10 16 kg-m 2 /s 2 = 1 kg 21. As the speed of a massive particle approaches the speed of light, the relativistic mass of the particle a. approaches the rest mass. b. does not change. c. increases without bound. d. increases slightly. e. decreases to zero. This is why the speed never reaches the speed of light. The particle becomes arbitrarily more massive as the speed approaches the speed of light, a constant force produces less and less acceleration (change in speed). 6