Answers
Chapter 25 - Music and Resonance
1. Find answer in first two sections of chapter.
2. 1.95 Hz
3.
4. Easier. Damping makes it so that the driving frequency doesn't need to be as closely matched to the resonant frequency.
5. No. Sound has very little energy.
6.
7. To maximize the likelihood that two notes played in unison sound good together.
8. root harmonics: f, 2f, 3f, 4f, ... The perfect 5th is 3f/2. its harmonics are 2(3f/2), 3(3f/2), etc. Every third harmonic of the root is the same frequency as every second harmonic of the perfect 5th.
9. No. They are two traveling waves going in opposite directions that meet and give the illusion of a wave standing still. See text.
10. A doubly reflected wave will be out of phase with the wave that initiated the process. That wave will reflect twice more and be out of phase by twice as much. Ultimately, represented as phasors, we'd have lots of them all with a slight rotation with respect to one another such that they cancel.
11.
12.
13. A pitch of 221 Hz with a beat frequency of 2 Hz.
14. 628 Hz
15. 500 Hz in front of you and 415 Hz as it drives directly away.
16. 1008 Hz at (x,y)=(60,5) and 992.2 Hz at (40,5).
17. 340 m/s.
18.
Chapter 28 - Quantum Mechanics
- Plug it in like we did in class.
- , but know how to find these energies.
- The probability to find the particle in any small region of width dx=finite will be the same everywhere inside the box as one would expect in the macroscopic realm.
- L/2
- don't worry about this one. didn't discuss the momentum operator.
Chapter 29 - Special Relativity
- That the value of quantities that we commonly measure is relative to the frame of reference.
- Yes, just not in vacuum.
- No. That was precisely the thought that drove Einstein to develop SR.
- That c+c=c, and other such cases.
- No. Energy conservation is, and accounts for mass in the form of rest energy.
- Absolutely not.
- The hotter water has more energy and thus more associated mass, since mass is really just localized energy.
- c
- v=0.999 999 963c
- 20 years.
- 0.141 c
- They are unchanged
- See notes. Did it in class.
- 0.866c
- 5.08 MeV/c
- 2.06 eV/c (easiest units if you use hc=1240 eV nm)
- 4.55x1017 photons/s
Fundamental Physics
- around 1015
- A distance at which the interaction changes.
- An experiment in which a target is bombarded by probe particles and the interaction is studied by the scattering angles of the probe particles.
- 7.44x10-15m
- 1.26
- 89.1 MeV; 7.42 MeV/nucleon
- Higher means more stable.
- The mass of the nucleons is always larger.
- 5,330 s
- 53,140 s
- Refer to links in the text.
- N/Z > 1 for larger nuclei
- 4.3 MeV
- 0.156 MeV
- 14.4 keV; difference is 1.95 meV (milli, not Mega) less since the atom carries this energy away as kinetic energy.