2. Physics 7C, Lecture 1 Winter Quarter -- 2007 Professor Robin Erbacher 343 Phy/Geo erbacher@physics.ucdavis.edu

3. Announcements Course syllabus (policy, philosophy) on the web: http://physics7.ucdavis.edu Quizzes every other lecture, ~20 minutes each, average of 4 best = 45% (or 20)% of grade. Final on Monday, March 19 10:30 am. If you cannot make this we suggest 7C in a different quarter. Quiz #1 next Wednesday, see calendar on web. Turn off cell phones and pagers during lecture.

4. Short Review of Physics 7B Simple Harmonic Oscillators We will see how oscillatory motion learned in 7B that we see in all vibrational systems gives us waves, important to much of the world around us. Two basic motions in nature: Linear or curvilinear (7B) Periodic motion (7B & 7C)

5. Simple Harmonic Oscillator (SHO)  Equlibrium Position The position at which all forces acting on an object sum to zero.  Displacement Change in the position of an object with respect to the equilibrium position.  Restoring Force Force that acts on the object that tends to make it move towards the Eq. position.  Simple Harmonic Motion When Restoring force proportional to the Displacement First, the ideas of SH Motion (SHM): The Constructs

6. SHO: Simple 2-d Pendulum Simple Harmonic Oscillators: Need restoring force F = -kx Restoring force proportional to displacement (for small enough displacements most oscillators obey SHM) Modeling Simple Harmonic Oscillators Begins with Newton’s 2nd Law: F = ma -g  = d 2  l dt 2 T mg mgcos  mgsin 

7. Periodic Functions What kind of function gives back the same function when differentiated twice? 22  T = 2  /b

8. Simple Harmonic Oscillators So, do we have the solution? We have: We want: … and … A generalized SHO solution is of the form: and:  Example: A pendulum in the playground…

9. Another SHO: Mass on a Spring Simple Harmonic Motion can be used to describe many phenomena A generalized solution is of the form: Hooke’s Law: Restoring force  spring constant k (determines pull) Displacement from Unstretched length … and …

10. Period Versus Frequency 22  Pendulum: Mass/Spring: How is the frequency f of the oscillations related to the period T? 1) f is proportional to T 2) f,T are inversely proportional 3) f is always twice T 4) f is not related to T 5) I have no clue 6) I’d like to buy a vowel Period:

11. To Summarize… y(t) = A sin (2  t/T +  ) y=Displacement A=Amplitude T=Period  =phase

12. Introduction to Waves Wave Phenomena We will see how waves are responsible for sound, light, propagation of information, and all of matter (when we get to quantum mechanics). A wave is a disturbance: a type of internal motion of a medium, in which the displaced portion returns to equilibrium. This disturbance propagates in space.

13. Waves in Nature A surfer braves the monster waves that form in an area on the north shore of Maui called “Jaws”, where about 12 times a year, the conditions are just right to produce some of the largest waves in the world: the shape of the beach sculpts the swells that originate from as far as Alaska into 40- to 70-foot [12- to 21-meter] walls of water. Steven Kornreich www.beachlook.com Thanks to Prof. Calderon who found this photo

14. Waves: Energy and Amplitude

15. Simple Waves What is a wave? Particles of the medium oscillate about their equil- ibrium positions in both a spatial and a temporal way. What other kinds of waves are there? Transverse Waves Longitudinal Waves Combo Waves (circular) Water Waves We will focus on these What is the simplest type of wave? A single wave due to a non-periodic disturbance: a traveling pulse wave.

16. Wave Parameters Certain independent parameters characterize all waves: 1)Amplitude: Controlled by the magnitude of the forces that started the wave. 2)Speed: Determined by the properties of the medium. 3)Direction: Determined by the direction of the forces starting the wave. Longitudinal: Oscillations in direction of wave velocity v Transverse: Oscillations are perpendicular to v 4)Frequency f of oscillations: Controlled by forces starting the wave. Wave: disturbance propagates in x…

17. Snapshot v. Movie Some waves are simply a pulse, and some are repetitive. These are harmonic (or sinusoidal), generated by SHOs. Harmonic waves have a dependent variable, wavelength, the distance at which the oscillation repeats. wavelength:  v wave /f 22 y(x) 22 y(t) Snapshot: Hold time constant, see where we are in space. Movie: Go forward in time, see how spatial points move.

18. The Wave Representation Describing the behavior of harmonic (sinusoidal) waves is extremely important in our physical world. The most general solution is of the form: Because there is both a time-dependence and a translation of the wave in space, we need to represent the wave using both t and x. What are all these parameters? x: location in the medium (spatial) t: time (temporal) T,f, period, freq., wavelength A: amplitude  phase Too complicated? Think of the sin argument as one big phase (or angle)   Total phase

19. Period, Frequency, Wavelength, Wave Speed period: frequency: wavelength: What’s the wave velocity? Ride the wave: constant  If we choose + in the wave function, the velocity is negative.

20. Particle Velocity So, the velocity of the wave, or propagating disturbance, can be found by riding along the wave at constant  : What is the velocity of a particle (or length of string) on the wave? As always: Why y? Transverse Waves: Particle moves as SHO! Note: I swapped x and t term. Block notes differ from DL expression. Both ok. Use DL version Mexican Wave!

21. Two Types of Wave Propagation Waves transfer energy without bringing along the mass. Particles get disturbed, collide, but stay oscillating about the equilibrium, they don’t move with the wave. But do all wave disturbances move perpendicular to direction of propagation? Transverse wave: particle motion is perpendicular to direction of propagation. Longitudinal wave: particle direction is same as (aLONG the) wave propagation

22. Longitudinal Waves Sound Waves The sound vibrations in 1-Dimension, such as long, narrow tubes, trombone, flute, trumpet, follows harmonic oscillations. But how does one describe the vibrations of the air? It’s all about pressure (density) fluctuations! Equilibrium = Atmospheric (or surrounding) pressure

23. Power and Intensity Sound is a pressure fluctuation in a medium. Sound energy is transported through the medium via these fluctuations. Power: sound energy time emitted by a source Intensity: P source area (area of wavefront)

24. How About Light? What kind of wave is a light wave? It’s a transverse excitation, perpendicular to the direction of wave propagation. What’s the medium that’s displaced as the wave propagates? Nothing! Light propagates via oscillating electric and magnetic fields (more on this later in the course!) The Enigmatic Ether!

25. Light: Visible, and Invisible The light we see is a small portion of the radiation that exists! Visible Light: 4.3-7.5 x 10 14 Hz Ultra Violet (UV) X-rays/   rays Infra Red IR  wave, AM/FM, TV frequency wavelength

26. Light: Visible, and Invisible The light we see is a small portion of the radiation that exists! Visible Light: 4.3-7.5 x 10 14 Hz Ultra Violet (UV) X-rays/   rays Infra Red IR  wave, AM/FM, TV frequency wavelength