Physics H133: Problem Set #2

Two-Minute Problems

Remember to give a good explanation, no longer than two sentences.

1. Q2B.8: Is a deep voice dominated by long or short wavelengths? How about a high voice? What does the wavelength have to do with how well the sound carries around a corner?
2. Q2S.4: You would not hear music where the sound waves from the two speakers are exactly out of phase. Where does this happen if you've reversed the wires? Would the waves be out of phase everywhere in the room?

Chapter Q2 Problems

• Q2S.1: Is this diffraction or two-slit interference? Again, draw a good picture! Be careful of whether you want constructive or destructive interference for the different parts of the problem.
• Q2S.6: Why do the sound waves spread? Within what angle is most of the sound power concentrated? If it widens 5m in traveling 100m, what is the corresponding angle? (It helps to draw a picture!) Remember that the speed of sound is about 343 m/s.
• Q2S.7: This is similar to Q2S.6. Draw a good picture so you can identify the appropriate angle in terms of how far away you are and how far you walk past the door. To what does the partially open door correspond?
• Q2A.1: At angle theta, what is the extra path length that one of the waves takes compared to the other? You can use this to find the phase difference Phi between the waves (Phi/2 pi = path difference/wavelength). Write waves from slits one and two so that they are out of phase by Phi and then add them together, using trig identities for the sin of a sum or difference of angles. It's easiest (by far) to split the path difference of Phi between the two waves, assigning +Phi/2 to one and -Phi/2 to the other.
• Q2R.1: Think about this as a two-slit interference problem, where you are locating places where the interference is totally constructive or destructive, based on path differences. (But note that the sounds are not actually interfering; it is only the timing of when the foghorn sounds you care about.)