**Traveling Waves**

**Example 3**

**Your turn Knowing:**

**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 = vt 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 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."**