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Welcome to Physics 7C!. Lecture 2 -- Winter Quarter -- 2005 Professor Robin Erbacher 343 Phy/Geo erbacher@physics.ucdavis.edu. Announcements. Course policy and regrade forms on the web: http://physics7.ucdavis.edu Quiz today! ~20 minutes long.

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welcome to physics 7c

Welcome to Physics 7C!

Lecture 2 -- Winter Quarter -- 2005

Professor Robin Erbacher

343 Phy/Geo

erbacher@physics.ucdavis.edu

announcements
Announcements
  • Course policy and regrade forms on the web:
  • http://physics7.ucdavis.edu
  • Quiz today! ~20 minutes long.
  • Reminder: Friday is “Academic Monday”. Monday DL’s: please attend DL this Friday. Friday DL’s are canceled. See calendar on website.
  • Final on Saturday, March 19 1:30pm. Let me
  • know this week if you cannot make this.
  • Turn off cell phones and pagers during lecture.
simple harmonic oscillators

2

A generalized solution

is of the form:

Simple Harmonic Oscillators

Pendulum:

Mass/Spring:

simple 1d waves

We will focus on these

Combo

Waves

(circular)

Transverse

Waves

Longitudinal

Waves

Water

Waves

Simple 1D Waves

What is a wave?

A wave is a type of internal motion of a medium, in which the displaced portion returns to equilibrium. This disturbance propagates in space as well.

Particles of the medium oscillate about their equilibrium positions in both a spatial and a temporal way.

What kind of waves are there?

wave parameters

Wave: disturbance

propagates in x…

Wave Parameters

Certain independent parameters characterize all waves:

  • Amplitude:Controlled by the magnitude of the forces that started the wave
  • Speed:Determined by the properties of the medium.
  • 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
  • Frequencyf of oscillations: controlled by forces starting the wave

Need y(x,t) !

snapshot v movie

y(x)

y(t)

2

2

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:

vwave/f

Movie:Go forward in time, see how spatial points move in SHM.

Snapshot:Hold time constant, see where we are in space.

the wave representation

The most general

solution is of the form:

Note: I swapped x and t term. Block notes differ from DL expression. Both ok. Use DL version

Too complicated? Think of the sin argument as one big phase (or angle) 

The Wave Representation

Describing the behavior of harmonic (sinusoidal) waves is extremely important in our physical world.

Because there is both a time-dependence and a translation of the wave in space, we need to represent the wave using both t andx.

What are all these parameters?

x: location in the medium (spatial)

t: time (temporal)

T,f, period, freq., wavelength

A: amplitude

 phase

total phase of the wave

Total phase

Total Phase of the Wave

If we hold x constant, the wave will repeat in T seconds.

If we hold t constant, the wave will repeat in  meters.

T and  play similar roles in the wave function, determining

how often the wave will repeat in time and space.

Wave: a displacement in space and time. The angle, , found from (T, , x, t, ), determines the total displacement y(x,t).

period frequency wavelength wave speed

period:

wavelength:

frequency:

What’s the wave velocity?

Ride the wave: constant 

If we choose + in the wave function, the velocity is negative.

Period, Frequency, Wavelength, Wave Speed
particle velocity

So, the velocity of the wave, or propagating disturbance, can be found by riding along the wave at constant :

As always:

Transverse Waves:

Particle moves as SHO!

Note: I swapped x and t term. Block notes differ from DL expression. Both ok. Use DL version

Particle Velocity

What is the velocity of a particle

(or length of string) on the wave?

Why y?

sound waves

Longitudinal

Waves

Equilibrium = Atmospheric (or surrounding) pressure

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!

power and intensity

Power:sound energy

time

emitted by a source

Intensity:Psource

area

(area of wavefront)

Power and Intensity

Sound is a pressure fluctuation in a medium. Sound energy is transported through the medium via these fluctuations.

how about light

The Enigmatic Ether!

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!)

light visible and invisible

frequency

Infra Red IR

wave, AM/FM, TV

Ultra Violet (UV)

X-rays/rays

wavelength

Light: Visible, and Invisible

The light we see is a small portion of the radiation that exists!

Visible Light:

4.3-7.5 x 1014 Hz

wave interference

y(wave1+wave2) = A1+A2

Wave Interference

What happens when there is more than one wave?

When two or more waves meet, they interfere with each other.

Combining waves by adding them is known as superposition.

Consider two waves on a string. What’s the maximum displacement of the string from equilibrium?

In Phase:1 - 2 = n2(n=integer)

(constructive interference)

Out of Phase:1 - 2 = [(2n-1)/2]2(n=integer)

(destructive interference)

superposition of waves

Adding 1D Waves Together:

Using the Full Expressions:

Superposition of Waves

What determines the total excursion of the medium at arbitrary time and position?

Phase angles and amplitudes!