1. Today 1/24  HW: 1/23 Handout “Beats and Boundaries” due Wednesday 1/29  Today: Beats 17.4 Reflections at Boundaries 27.3  Monday: Thin Film Interference 27.3  Labs start Monday

2. Next Week’s Lab: Microwaves  A wave in the “electric field”  Reflection and transmission from and through wood  Reflection from metal (why metal is bad in your microwave)  Polarization (see section 24.6)  Interference (Young’s Double Slit)

3. Beats  Occur when the frequencies of the sources are not the same  Frequencies must be close  Locations for constructive interference move over time  Causes sound to get loud and soft  f b “beat frequency” depends on source frequency difference

4. 0.5 s 10 Hz 12 Hz 2 Hz

5. Sources emitting different frequencies. Source 1Source 2 In this case they are alternately in and out of phase as time goes by.

6. Source 1Source 2 Sources emitting different frequencies. In this case they are alternately in and out of phase as time goes by.

7. Source 1Source 2 Sources emitting different frequencies. In this case they are alternately in and out of phase as time goes by.

8. Source 1Source 2 Sources emitting different frequencies. In this case they are alternately in and out of phase as time goes by.

9. Source 1Source 2 Sources emitting different frequencies. In this case they are alternately in and out of phase as time goes by.

10. Source 1Source 2 Sources emitting different frequencies. In this case they are alternately in and out of phase as time goes by.

11. Source 1Source 2 Sources emitting different frequencies. In this case they are alternately in and out of phase as time goes by.

12. Source 1Source 2 Sources emitting different frequencies. In this case they are alternately in and out of phase as time goes by.

13. Source 1Source 2 Sources emitting different frequencies. In this case they are alternately in and out of phase as time goes by. c

14. Source 1Source 2 Sources emitting different frequencies. In this case they are alternately in and out of phase as time goes by. c

15. Source 1Source 2 Sources emitting different frequencies. In this case they are alternately in and out of phase as time goes by. c

16. Source 1Source 2 Sources emitting different frequencies. In this case they are alternately in and out of phase as time goes by. c

17. Source 1Source 2 Sources emitting different frequencies. In this case they are alternately in and out of phase as time goes by. c

18. Source 1Source 2 Sources emitting different frequencies. In this case they are alternately in and out of phase as time goes by. c

19. Source 1Source 2 Sources emitting different frequencies. In this case they are alternately in and out of phase as time goes by. c

20. Source 1Source 2 Sources emitting different frequencies. In this case they are alternately in and out of phase as time goes by. c

21. Source 1Source 2 Sources emitting different frequencies. In this case they are alternately in and out of phase as time goes by. c Now the locations of constructive (and destructive) interference move in time. A stationary listener hears “Beats.”

22. Beats f b =  f 1 - f 2  The beat frequency tells you the difference between the two source frequencies.

23. You want to know the frequency of a tuning fork. You test it by playing it at the same time as a tuning fork with a known frequency of 342 Hz and you hear beats at a rate of 5 per second. You then play it at the same time as one with a known frequency of 349 Hz and the beats are heard at a rate of 12 per second. What is the frequency of the tuning fork? a. 347 Hz b. 361 Hz c. 345.5 Hz d. 337 Hz e. 354 Hz.

24. Reflections at Boundaries  Four situations Fixed end Free end Light to heavyHeavy to light

25. Fixed End Reflections Fixed end Crest turns into trough Leading edge is the same See “Wave Interference” handout for how the string looks during the reflection. Same velocity, length, and amplitude

26. Free End Reflections Free end Crest stays a crest Leading edge is the same See “Wave Interference” handout for how the string looks during the reflection. Same velocity, length, and amplitude

27. Light to Heavy Both transmission and reflection Boundary feels like a fixed end to the light string Reflection just like fixed end, inverted Transmitted wavelength has the same shape except it’s shorter in length because it travels slower than the incoming wave. Slower, so not as far from boundary Shorter, “bunched up”Inverted wave

28. Heavy to Light Both transmission and reflection Boundary feels like a free end to the heavy string Reflection just like free end, not inverted Faster, farther from boundary Longer, “spread out”Wave not inverted Transmitted wavelength has the same shape except it’s longer in length because it travels faster than the incoming wave.

29. Slower, so not as far from boundary Shorter, “bunched up”Inverted wave Faster, farther from boundary Longer, “spread out”Same as incoming wave Light: GlasstoAir Light: AirtoGlass