1. Average: 51.2/78 = 65.6 %

2. Traveling waves

3. Provide as concise a definition for the phase angle of a wave as you can manage.
The phase angle (phi) is a value that can be chosen so that the function gives some other displacement and slope at x=0 when t=0. (7)
the angle between a point on the wave and a reference point (5)
The phase angle is determined by kx-wt as determined by sine or cosine. Depends on the oscillation of and describes the linear movement of the wave it terms of time. (1)
An angle that changes linearly with time and position and that describes the “point” within a period at which an oscillating system finds itself (the argument of the sinusoid).

4. Chapter 16 Problems

5. Chapter 16 Problems

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

7. Extra Office Hours Exam Week
Monday (28 April): 1:30 to 3:30
Tuesday (29 April): 11:00 to 12:00 and :30 to 3:30
Final Exam is at 8:00-10:00 on Wednesday 30 April 2008 in SW 007

8. Two waves are traveling along within the same medium
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? (1:1--1;2:1—13; 4:1—6; other--4; no answer—17)
The rate ought to be twice as large when compared to the rate of a single wave traveling in that direction. [the amplitude is doubled, but pay attention to the question!]
The energy transfer while having two waves together is going to be four times that of a single wave. [Correct, but some more explicit explanation would have been nice.]

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. Chapter 16 Problems

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

14. 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).

15. Chapter 16 Problems

16. Standing waves

17. Reflections at a Boundary

18. 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?

19. 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?

20. 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 occurs because the string elements oscillate parallel to the y-axis. However, the air elements oscillate parallel to the x-axis as the wave travels through air, and oscillates parallel to the x-axis. (The oscillations of both waves are in the same direction, the propagation direction is different!)
The transverse wave in the violin makes a sound wave, which is a longitudinal wave, by literally pushing against the air near the string. This makes the air move in a sound wave. (~ 6 were like this; the key is that the two waves are in different media, and the sound leaves the string in the direction of the string’s vibration (more or less))

21. Sound waves I = ½ rw2sm2vs = ½(Dpm)2/vsr Dpm = rwsmvs 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!
I = ½ rw2sm2vs = ½(Dpm)2/vsr
Dpm = rwsmvs

22. Earthquakes: Sound waves in the Earth (did anyone feel the quake this AM?)
In most solids, longitudinal (P above) waves travel faster than transverse (S)
Waves since the bulk modulus is bigger than the shear modulus.

23. Earthquake felt in Bloomington 18 April 2008
Magnitude: 5.2

24. WAVES II--SOUND Material Velocity of Sound Air (0oC) 331 m/s
Helium (20oC)
965 m/s
Water (0oC)
1402 m/s
Water (20oC)
1482 m/s
Seawater (20oC ?)
1522 m/s
Aluminum
6420 m/s
Steel
5941 m/s

25. Chapter 17 Problems NOTE: r=1.21 kg/m3 v=343 m/s At T=20oC
FIRST: What is the ratio of the Intensities between the two cases?
e). What is the pressure difference that corresponds to each of these intensities?

26. Chapter 17 Problems

27. Standing waves: Pipes
The resonance frequencies of pipes depend on the conditions at the two ends. A closed end needs a NODE, and an open end needs an ANTINODE.
The book gives you formulae for the two cases that you can remember, OR you can just remember these two conditions and draw pictures! (I find this way of doing it MUCH easier.)

28. Chapter 17 Problems