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# PH 223 20.1-20.3

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## Richard Datwyler

on 13 September 2016

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#### Transcript of PH 223 20.1-20.3

Traveling Waves
Example 3
What happens to the velocity if I increase the tension by factor of four?
Slide 20-40

Visualizing a Longitudinal Wave

Slide 20-32

An Alternative Look at a Traveling Wave

Slide 20-4

Chapter 20 Preview

Slide 20-3

Chapter 20 Preview

Slide 20-49

QuickCheck 20.6

The period of this wave is

1 s.
2 s.
4 s.
Not enough information to tell.

Slide 20-47

Sinusoidal Waves

Slide 20-46

Up.
Down.
Right.
Left.
Zero. Instantaneously at rest.

QuickCheck 20.5

A wave on a string is traveling to the right. At this instant, the motion of the piece of string marked with a dot is

Slide 20-44

Sinusoidal Waves

Above is a snapshot graph for a sinusoidal wave, showing the wave stretched out in space, moving to the right with speed v.
The distance spanned by one cycle of the motion is called the wavelength  of the wave.

Slide 20-42

A wave source at x = 0 that oscillates with simple harmonic motion (SHM) generates a sinusoidal wave.

Sinusoidal Waves

Slide 20-23

A Longitudinal Wave

Slide 20-21

The Wave Model

Slide 20-6

Chapter 20 Preview

Slide 20-43

Sinusoidal Waves

Above is a history graph for a sinusoidal wave, showing the displacement of the medium at one point in space.
Each particle in the medium undergoes simple harmonic motion with frequency f, where f = 1/T.
The amplitude A of the wave is the maximum value of the displacement.

Slide 20-31

This graph tells the history of that particular point in the medium.
Note that for a wave moving from left to right, the shape of the history graph is reversed compared to the snapshot graph.

A graph that shows the wave’s displacement as a function of time at a single position in space is called a history graph.

History Graph

Slide 20-30

The figure shows a sequence of snapshot graphs as a wave pulse moves.
These are like successive frames from a movie.
Notice that the wave pulse moves forward distance x = vt during the time interval t.
That is, the wave moves with constant speed.

One-Dimensional Waves

Slide 20-29

Snapshot Graph

Slide 20-28

Increased by a factor of 4.
Increased by a factor of 2.
Decreased to one half its initial value.
Decreased to one fourth its initial value.
Not possible. The pulse speed is always the same.

QuickCheck 20.2

Slide 20-27

Increased by a factor of 4.
Increased by a factor of 2.
Decreased to one half its initial value.
Decreased to one fourth its initial value.
Not possible. The pulse speed is always the same.

QuickCheck 20.2

Slide 20-22

A Transverse Wave

A sinusoidal wave moves forward one wavelength (2 m) in one period.

Slide 20-50

QuickCheck 20.6

The period of this wave is

1 s.
2 s.
4 s.
Not enough information to tell.

Slide 20-48

Sinusoidal Waves

The distance spanned by one cycle of the motion is called the wavelength  of the wave. Wavelength is measured in units of meters.
During a time interval of exactly one period T, each crest of a sinusoidal wave travels forward a distance of exactly one wavelength .
Because speed is distance divided by time, the wave speed must be:

or, in terms of frequency:

Slide 20-45

Up.
Down.
Right.
Left.
Zero. Instantaneously at rest.

QuickCheck 20.5

A wave on a string is traveling to the right. At this instant, the motion of the piece of string marked with a dot is

Slide 20-41

When describing a wave mathematically, we’ll use the generic symbol D to stand for the displacement of a wave of any type.
D(x, t) = the displacement at time t of a particle at position x.

In “the wave” at a sporting event, the wave moves around the stadium, but the particles (people) undergo small displacements from their equilibrium positions.

The Displacement

Slide 20-26

vA > vB
vB > vA
vA = vB
Not enough information to tell.

QuickCheck 20.1

Slide 20-25

vA > vB
vB > vA
vA = vB
Not enough information to tell.

QuickCheck 20.1

Slide 20-24

Wave Speed

Slide 20-37

B.

C.

D.

A.

QuickCheck 20.3

This is a snapshot graph at t = 1 s of a wave pulse traveling to the right at 1 m/s. Which graph below shows the wave pulse at t = –1 s?

Slide 20-36

B.

C.

D.

A.

QuickCheck 20.3

This is a snapshot graph at t = 1 s of a wave pulse traveling to the right at 1 m/s. Which graph below shows the wave pulse at t = –1 s?

A transverse wave has the displacement perpendicular to the direction of travel.
A longitudinal wave has the particles move in the direction of travel.
Here 'mu' is the string's mass density
Speed of a wave on a string
With T as tension
These two pulses travel on
the same stretched string.
Which is true?
A
B
C
D
These two pulses travel on
the same stretched string.
Which is true?
A
B
C
D
Speed depends on the property of the medium
not the amplitude
A
B
C
D
E
For a wave pulse on a string to travel twice as
fast, the string tension must be:
For a wave pulse on a string to travel twice as
fast, the string tension must be:
A
B
C
D
E
A graph that shows the wave's displacement as a function of position at a single instant.
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Snapshots can be tricky.
Lets try this by an experiment.

"Can all things be represented in the form of waves?"
" I'm having a hard time visualizing longitudinal waves. what does a longitudinal wave physically look like?"

"I have some questions about differentiating between history and snapshot graphs, but I think they'll make more sense after we talk about them in class."

" I Think the equations presented will be the most confusing for me and I will need a little more clarification to understand them completely."
"I didn't understand the graphs very well, and the section on Sinusoidal waves was also confusing."
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