Modern Physics

Fall 2009

Start reading chapter 2 on relativity by Monday, Sept. 21.

Homework Assignment 2: Due Friday, September 25?

1. A source (e.g. a bat) emits sound at a frequency of 1000Hz. It is moving toward a bug at a speed of 20m/s. The bug is moving away from the bat with a speed of 10m/s. The bat hears the waves reflected from the bug. What is the frequency it hears if the speed of sound is 340m/s.

2. Two speakers emit sound at the same frequency and in phase with each other. A person stands 7m from one speaker and 5m from the other. What is the lowest audible (20Hz-16kHz) frequency for destructive interference at the person, i.e. so the sound level is a minimum.

3. Light of wavelength of 0.6mm goes through a single slit of unknown width. The spacing between the two dark spots on either side of the central maxima of the diffraction pattern is 0.01m on a screen 2m away from the slit. What is the width of the slit? (The diffraction for light is the same as it is for sound.)

4. Light of unknown wavelength illuminates a double slit of separation 60mm. (Assume the slits are very narrow – so you do not have to worry about diffraction minima in the patterns.) The distance between the first and third maxima, beyond the central maximum, is 0.02m when the screen is 1.5m from the slits. What is the wavelength of the light?

5. The first three natural (resonant) frequencies of an organ pipe are 300Hz, 900Hz and 1500Hz. How long is the tube, and is it open or closed?

6. An ultrasound emitter has a frequency of 50kHz. Sound is reflected off a person walking away from the emitter. If the reflected sound is added to the original 50kHz signal, a beat frequency of 150Hz is produced. How fast is the person walking? Use c_sound = 340m/s. (You can assume v/c <<1.)

7. You shine light of wavelength 500nm on a diffraction grating and the spacing between the second bright spot and the central maximum is 0.15m on a screen 1.2m from the grating. What is the spacing of the “lines” on the grating?