c(light in air) = 3x108 m/s c(sound in classroom air) = 341 m/s n(water) = 1.33 f(microwave oven) = 2450 MHz h = 6.6x10‐34 J/Hz Q(electron) = 1.6x10‐19 Coulombs n(diamond) = 2.5 1. A 341 Hz tuning fork resonates at what wavelength of sound in a column of class room air 25 cm long? Λ=c/f=341/341=1m. I gave the 25 cm which is what you would measure in the lab experiment we did=1/4 λ. You did not need it here. 2. Two tuning forks as in problem #1 are made to oscillate in phase. One is 1.5 m directly in front of you and the other 2.0 m in front of you. What do you hear? Explain, perhaps drawing a picture. The tuning forks send sound from positions ½ λ apart, so they DESTRUCTIVELY interfere, cancelling each other, so that you hear no sound. 3. How far apart are the hot spots when cooking in a microwave oven (no turn table)? Show your calculation. λ/2=c/f/2=3x108/2450x106/2=6 cm (λ/2 because that is the distance between maxima in the standing wave). 4. What is the momentum p (in Kg m/s) of the photon in problem #7? Show your logic in case you got #7 wrong. Hint: If you use one system of units (m, s, Coulombs, Hz) it will come out correctly. p=E/c=hf/c=h/λ=6.2x10‐34/6x10‐2=1x10‐32kg‐m/s 5. A standing wave is composed of how many waves doing what? Be specific. 2 waves of same f moving in opposite directions. 6. Give an accurate definition of Absolute Zero. What is its temperature in Kelvin? Theoretically the temperature at which the
volume of a gas reduces to zero; T(absolute zero)=0 K.
7. We used Charles’ Law in determining absolute zero in the lab. State Charles’ Law. The change in the volume of a gas is
proportional to the change in its temperature.
8. Name 3 temperature scales. Kelvin, Celsius, Fahrenheit
9. Define an inertial reference frame. Inertial frame is one which is not accelerating.
10. Katy observes 2 events which are 1 second apart. Ben is traveling by her at a speed of 0.9c. Does Ben see the two events 1
sec, more than 1 sec, or less than 1 sec apart? Explain. For extra credit (2 pt.), calculate the time interval between the events
that Ben experiences. Katy’s time is the proper time=1 sec, which is the shortest time that can be measured, so Ben measures
a time > 1 sec. γ=1/sqrt (1-v2/c2)=1/sqrt(1-.81)=1/0.44=2.3 so t(Ben)=2.3 sewc.
11. Cady observes 2 events which are 1 meter apart. Percy is traveling by her parallel to the meter stick at a speed of 0.5c. Does
Percy see the two events one meter, more than one meter, or less than one meter apart? Explain. For extra credit (2 pt.),
calculate how far apart in space Percy sees the events. Because Percy’s frame is moving parallel to Cady’s meter stick, he
sees it contracted by L/γ =1*sqrt(1- v2/c2) = sqrt(1-0.25) = sqrt(0.75) = 0.87 m.
12. What measurement can one twin do to detect that he will be a different age than his twin when one travels to Mars and the
other stays on Earth? Note: the answer is not a use a clock. Extra credit (1 pt.): Which twin must do the experiment? The
twin who travels to Mars can use a pendulum to see he is accelerating (and decelerating) as he makes the round trip.
Therefore, he is the one moving and it is his biological clock which has time dilated with respect to his stationary brother or
sister.
13. What frequency photon is required to produce a proton/anti-proton pair at rest? Extra credit (1 pt.): In what part of the E-M
spectrum is it in? f = E/h = 2m(proton in ev)*Q(proton)/h = 2*938*106*1.6*10-19/6.2*10-34 = 4.8*1023 (extreme gamma ray)
14. State either the basic fact or principle upon which the special theory of relativity is based. All observers see light travel at the
same speed in vacuum (c).
15. State the other basic fact or principle upon which the special theory of relativity is based. There is no unique rest frame.
16. What is the value of your gamma (γ) if you are traveling at 0.8c? . γ=1/sqrt (1-v2/c2)=1/sqrt(1-.0.64) =1/sqrt(0.36) =1/0.6
=1.67
17. You travel in the x direction at the γ of problem #16. You pass a meter stick which lies along the y axis, perpendicular to
your direction of travel. How long does the meter stick look to you? 1m since it is perpendicular to your travel.
18. Who invented the first artificial ice machine? John Gorrie.
19. Is your chair in this classroom on the surface of the earth an inertial frame of reference? Explain you answer. The earth is
rotating about its north/south axis and revolving around the sun, so it is accelerating—hence NOT and inertial frame (like
how we feel when we are in a car going fast around a curve).