Ch14 Waves

Wave Types

Mechanical Waves: require a material medium to propagate.

Water Rope

Springs Sound

3 types of Mechanical Waves– Transverse– Longitudinal– Surface

Longitudinal Waves: The medium moves parallel to the direction of the wave.

Longitudinal Waves• A Longitudinal: A wave in which the vibration is in the same

direction that in which the wave is traveling.

• Notice how the atom in the box below never leaves the box even though the wave is obviously traveling to the right.

Animation courtesy of Dr. Dan Russell, Kettering University

Transverse wave: the medium vibrates perpendicularly to the direction of travel.

Transverse Mechanical Waves• A transverse wave is one in which the individual atoms or

particles vibrate in a direction perpendicular to the direction of motion of the wave.

• Notice how the atoms in the box below never leave the box even though the wave is obviously traveling to the right.

Animation courtesy of Dr. Dan Russell, Kettering University

Rotations

-1.5

-1

-0.5

0

0.5

1

1.5

0 0.2 0.4 0.6 0.8 1 1.2

t

As the Wheel Turns• Watch how the sine function (which demonstrates a

wave) traces out as a wheel turns.

• The vertical axis represents horizontal position and the horizontal axis represents time.

Rotations

-1.5

-1

-0.5

0

0.5

1

1.5

0 0.2 0.4 0.6 0.8 1 1.2

t

Simple Harmonic Motion

Simple Harmonic Motion: Motion caused by a linear restoring force that has a period independent of amplitude.

Period: The time required to repeat one complete cycle

Amplitude: Maximum displacement from equilibrium.

• Transverse wave: the medium vibrates perpendicularly to the direction of travel.

• The wave travels horizontally. Any one point on the wave travels vertically

Transverse Wave

e.g.

Pianos

Guitar String

Standing Waves

Longitudinal Waves: The medium moves parallel to the direction of the wave.

The wave travels horizontally. Any one point on the wave also travels horizontally.

Surface Wave• Surface Waves: Are a mixture of both

parallel and perpendicular motion.

HW

Read CH14

Worksheet vibrations and Waves 1-8

Wave Pulse• Wave Pulse: A single disturbance that travels

through a medium

• A pulse can move in either direction

Hand Drawn Examples

• Transverse

• Longitudinal

• Pulse

• Period (T): The shortest time interval during which motion repeats.

Measures of a Wave

Time (s)

1 2 3 4 5 6 7 8

• Frequency (f): The number of complete vibrations per second.

Measures of a Wave

0.2 0.4 0.6 0.8 1.0 1.2 1.6 1.8

Time (s)

Number of vibration (cycles)

1 2 3 4 5

Measures of a Wave• Wavelength : The shortest distance

where the pattern of the wave repeats

Meters (m)

.01 .02 .03 .04 .05 .06 .07 .08

( )

(.7 .3 )m m .5 .1m m .4m (.8 .4 )m m

Measures of a Wave• Crest: The highest point on a wave• Trough: The lowest point on a wave

.01 .02 .03 .04 .05 .06 .07 .08

Measures of a Wave• Amplitude: The maximum displacement from

rest or equilibrium

.01 .02 .03 .04 .05 .06 .07 .08

Wave Examples• Can two waves can have the same

wavelength and velocity, but different amplitudes?

.01 .02 .03 .04 .05 .06 .07 .08

The greater the amplitude the greater the energy.

Waves• When these oscillations between two extremes are graphed wrt time, we

see the following profile emerge.

• The Wavelength () is the distance from the “same” point on two consecutive oscillations.

• The Amplitude (A) is the maximum displacement from zero.

• The Period (T) is the time between the same position on consecutive “humps.”

• The Frequency (f) describes how often an oscillation occurs.

• The high points on the wave are known as “crests.”

• The low points on the wave are known as “troughs.”

0

+A

-A

Wave Velocity

msv

T

1fT

v f

The velocity of a wave is the distance traveled divide by the time it takes to move

Example• A sound wave from a starters pistol is heard

100m down the track at the finish line. a) How long did it take the starter to start the stop

watch if he waited for the sound.b) How long if he started the stopwatch when he

saw the smoke?c) How much faster do the runners times appear?

343 msound sv

83.0 10 mlight sv x

Example WS14.2 #1

• A sound wave produced by a clock chime 515m away is heard 1.5s later.

a) What is the speed of sound in air?

b) The sound wave has a frequency of 436Hz. What is its period?

c) What is its wavelength?

Practice Problems

• WS 14.2– #’s 2,3

• WS 14.3– #’s 1,2

Wave Boundaries

• What happens when a wave hits a boundary between two mediums?– Part of the wave is transmitted– Part is reflected

• The amount that gets transmitted versus reflected depends on the difference between two mediums.

Wave Boundaries

• When a wave is transmitted from less dense to more dense, the reflected wave is inverted.

Wave Boundaries

• Reflection follow Newton’s 3nd Law– The string pulls up on the wall– The wall pulls down on the string– The wall doesn't move– The string is reflected inverted.

Wave Boundaries example• A pulse is sent along a spring. The spring is

attached to a light thread which is attached to a wall.

a) What happens when the pulse reaches the string?

b) Is the pulse reflected erect or inverted?c) What happens when the transmitted pulse

reaches the wall?d) Is this pulse erect or inverted?

Waves at BoundariesWaves at Boundaries

Reflected pulse

Transmitted pulse

Low Density Medium High Density Medium

Note: Both amplitudes get smaller

Wave Boundaries example• A pulse is sent along a light thread. The

thread is attached to a spring which is attached to a wall.

a) What happens when the pulse reaches the spring?

b) Is the pulse reflected erect or inverted?c) What happens when the transmitted pulse

reaches the wall?d) Is this pulse erect or inverted?

Waves at BoundariesWaves at Boundaries

High Density Medium Low Density Medium

Reflected pulse

Transmitted pulse

Wave Boundaries

• The frequency of a wave being transmitted from one medium to another does NOT change.

• e.g. If I’m moving a string up and down, I don’t change the velocity that I vibrate it.

Wave Demo’s

• Spring to a fixed boundary (more dense)

• Spring to a light string (less dense)

• Light string to spring

• Heavy spring to slinky.

Practice Problems

• Page 296– #’s 5-8

Superposition of Waves

• Principle of superposition:

• Interference:

• Constructive Interference:

• Destructive Interference:

• Record these vocabulary terms and define their meaning using your text.

Superposition of Waves

• Principle of superposition: The displacement of a medium caused by two or more waves is the algebraic sum of each wave.

• Waves pass each other so the original wave continues unaltered.

• Interference is the result of the superposition of two or more waves.

Wave Superposition

Constructive Interference

2 or more waves adding together to make a larger wave

Antinode is the point of maximum displacement (i.e., where amplitude is largest)

Wave Superposition

DestructiveInterferenceConstructive Interference NodesAntinodes

The blue wave below represents the sum of the 2 other waves.

Wave Superposition

Graph A

Wave Sum

Constructive InterferenceConstructive InterferenceDestructive InterferenceDestructive Interference

Antinodes

AntinodesAntinodes

NodesNodes

Interference of Sine Waves• When two or more waves occur in close proximity to one

another, they produce interference patterns.

• Constructive Interference

• Destructive Interference

0

+A

-A

Superposition of Waves

• Constructive Interference: Occurs when the displacements are in the same direction

• Destructive Interference: Occurs when the displacements are on opposite sides of equilibrium.

• Show excel demo

Practice Problems• Sketch the resultant

waveform when the center of the two waves are at the red boundary

Superposition of wavesNode

Node

Node

Node

Practice Problems

• WS 14.1– # 9– WS 14.4 1-6

End Ch 14

• Chapter Quiz

• Moved standing waves to ch15

Standing Waves

• Standing Wave:

• Node:

• Antinode:

• Record these vocabulary terms and define their meaning using your text.

Standing Waves

• Standing Wave: has stationary nodes and antinodes. It is the results of identical waves traveling in opposite direction.

• Node: The medium is not displaced as the waves pass through

• Antinode: The displacement caused by interfering waves is largest.

Standing Waves

• In order for a standing wave to exist, there must be an identical wave traveling in the opposite direction

• Standing wave demo

Standing Waves

Harmonics: Standing wave that consist of more than one pulse

Standing waves• Fundamental Frequency: The lowest frequency

that creates a standing wave in a given medium.

• Harmonics (overtones): frequencies with integer multiples of the fundamental frequency.

• These frequencies make up the harmonic series.

Harmonic Series in a string

1

2

2

2

3

2

Length L

1,2,3...2

vfn n n

L

Reflection of Waves

• Normal

• Angle of incidence

• Angle of reflection

• Law of reflection

Diffraction Waves

• Node

• Antinode

• demo

Conservation of Energy Intro WS #2

PE

PE + KE

KE

PE + KE

PE

4

Reflected

Transmitted

superposition

A A

B B