Average: 48.3/78 = 61.9 %

1. Average: 48.3/78 = 61.9 %

2. Konopinski Public Lecture “From the Big Bang to the Nobel Prize” John Mather Whittenberger Auditorium in the IMU 7:30 PM Tuesday

3. Traveling waves

4. Provide as concise a definition for the phase angle of a wave as you can manage. • Phase angle is how the wave varies from what it normally looks like. Knowing the phase angle allows you to find x (8 answers, like this one, left me wondering just what the student had in mind) • The phase angle of a wave, phi, is chosen so that the displacement at t=0 is not necessarily zero. (6, answers concentrated on what I call the phase offset) • The phase angle describes the point at which a wave is in its period.(7, like this one really hit home) • An angle that changes linearly with time and position and that describes the “point” within a period at which an oscillating system finds itself (i.e. the argument of the sinusoidal function).

5. Chapter 16 Problems

6. Chapter 16 Problems

7. Chapter 16 Problems Be careful, remember to look carefully at what it plotted!!! What is T?? What is l??

8. Follow-up: Earthquakes http://en.wikipedia.org/wiki/Seismic_wave Vp = [(k + 2m/3)/r]1/2 Vs = (m/r)1/2; k – Bulk modulus; m – rigidity; r – mass density

9. Interfering waves If the medium is linear (most often the case), then the net medium displacement due to two or more waves is just the sum of the two individual displacements. (this is the case for all of our discussion in P221, but NOT for all things. Tsunamis, some laser phenomena etc. arise in non-linear media).

10. Interfering waves Add the blue and red waves together from the top panels

11. Interfering Harmonic Waves _ _ + (see page A-9 for this and many other trig identities.)

12. Two waves are traveling along within the same medium. Each wave has the same amplitude and along a particular direction in space they are observed to oscillate in phase with each other. What is the ratio of the rate at which energy is transferred by the combination of the two waves in this direction to that which would result from having only a single wave traveling in that direction?(2:1—20; 4:1—5; other--4; no answer—26) • Well, i suppose since the resulting wave would have twice the amplitude of the former waves. I would imagine that it would transfer energy twice as fast because the frequency remains the same but its delivering twice as much energy.[the amplitude is doubled, but pay attention to the question!] • Ratio=4/1; ym'=2ym(cos(1/2(phi))); (2ym)^2/ym^2=4 . [That sums up the right way to think of it pretty concisely !!]

13. Chapter 16 Problems

14. Interfering Harmonic Waves (reprise) + + _ _ + (see page A-9 for this and many other trig identities.)

15. Standing waves This can be thought of as either a resonance, or a case of interference between left-going and right- going waves in the same medium (it’s really both).

16. Standing waves

17. Example Stringed Instruments http://www.littlehandsmusic.com/Merchant2/graphics/00000001/Becker_Violin.jpg http://www.musicwithease.com/guitar-pictures.html

18. Chapter 16 Problems

19. Reflections at a Boundary

20. Standing waves Two strings with identical linear mass densities and lengths but different tensions. For each case which string has the greater tensions if the frequencies are the same?

21. Standing waves l l l l Two strings with identical linear mass densities and lengths but different tensions. For each case which string has the greater tensions if the frequencies are the same?

22. The standing wave set up on a violin string when it is bowed is a transverse wave, and yet the wave your ear hears (the musical note) as a result of this vibrating string, is a longitudinal wave. Explain briefly how a transverse wave can produce a longitudinal wave. • The transverse wave motion of the string causes compressions and expansions in the air surrounding it. These compressions and expansions form the longitudinal wave that is picked up by the tympanum in the ear. (True, and most said something like this; generally it shouldn’t be surpirsing that a transverse wave might produce a longitudinal wave). • This does not quite hit the message home; the difference is that the waves are propogating in different directions; the string sets up oscillating compressions and rarifractions that make up sound.

23. Sound waves You can think of a sound wave as an oscillating pattern of compression and expansion (DP), or as an oscillating position for small packets of air [s(x,t), which leads to the above picture]. REMEMBER this is a longitudinal wave! Dpm = rwsmvs I = ½ rw2sm2vs = ½(Dpm)2/vsr

24. WAVES II--SOUND