Chapter 19Chapter 19

Vibrations and Waves

• Vibration: A disturbance

“wiggle” in time.

•Wave: A disturbance in

space and time.

Oscillatory Motion

• The to-and-fro vibratory motion, such as that of a pendulum.

Simple Pendulum

g

L2P

For small displacements, the period of the simple pendulum is related to its length (L) and the acceleration due to gravity (g) by the following:

Simple Harmonic Motion

• is a type of oscillatory motion in

which the motion repeats itself.

•This motion is caused by a “restoring force” that acts in the opposite direction of the displacement.

Simple Pendulum

• Under small displacements, the simple pendulum behaves as a harmonic oscillator.

•For a pendulum, the “restoring force” is usually exerted by

GRAVITY

Amplitude

• The maximum displacement from some equilibrium (mid point) position.

(Applies to both vibrations and waves.)

Mass-Spring System is Another Example of a Simple Harmonic

Oscillator

Live Demonstration

Wavelength

• The distance between successive crests, troughs, or identical parts of a wave.

•Common symbol used for

wavelength is the Greek letter - pronounced “lambda”

Sine Curve

AmplitudeA

Wavelength Crest

Trough

• Frequency: The number of vibrations per unit time.

• Common symbols are f and the Greek

letter - pronounced ”nu”

•Period: The time in which a vibration is completed.

•Common symbols are T and the Greek letter - pronounced “Tau”

More on frequency

• We can talk about the frequency of a vibration or of a wave. Frequency is measured in inverse seconds, or Hertz (Hz).

•E.g..

•f = 10 cycles/sec = 10sec-1 = 10 Hz.

Frequency and Period are related

• Frequency equals inverse Period.

•Period equals inverse Frequency.

In symbols, this means...

f = 1/T or = 1/ and

T = 1/f or = 1/

Examples

AM radio frequencies are measured in KiloHerts - (KHz).

The period is 1/1,000Hz = 1x10-3 sec = 1millisecond (ms)

Kilo = one thousand = 1,000 = 1x103 .

• FM radio frequencies are measured in MegaHertz (MHz)

•The period is (1/1,000,000 Hz)=

1x10-6 sec = 1 microsecond (s).

•Mega = one million = 1,000,000 = 1x106

More Examples• Water waves might have a

frequency of 2Hz (i.e. 2 cycles per second).

•The corresponding period is equal to:

1/f = 1/2Hz = 0.5 seconds

• The AM and FM radio waves are examples of

• Light is another example of an

electromagnetic wave

•Electromagnetic Waves

The water waves are examples

of Mechanical Waves

Mechanical waves require a medium in which to propagate. Electromagnetic waves do not.

Wave Speed

• The speed with which waves pass a particular point.

•Common symbol used for

wavespeed is the letter v.

• Wavespeed = wavelength / period

v = f

but, since we already know that frequency is the same as inverse period ( f = 1/T), then we can also write this as

v = /T

•In symbols, this is:

A note as to why we use “v”

• The letter v is used for velocity in general.

•Velocity is speed in a specific direction.

•Velocity and speed are closely related.

For Example• If I tell you I’m traveling at

55 miles/hour due north, I

have told you my velocity

•If I tell you I’m traveling at 55 miles/hour, I have told you my speed.

Types of Waves

There are two types of waves

2)Longitudinal Waves.

1) Transverse Waves.

1) Transverse Wave:

A wave in which the vibration is in a direction perpendicular (transverse) to the direction in which the wave travels.

e.g. Light waves.Waves on a string.Seismic “S”-waves.

2) Longitudinal Wave:

A wave in which the medium vibrates in a direction parallel (longitudinal) to the direction in which the wave travels.

e.g. Sound.Seismic P-waves.

http://www.physics.ohio-state.edu/133/demo/Lwave.gif

In a longitudinal wave, the medium has regions of compression and expansion which are along the direction of wave propagation.

Regions of expansion are also called (rarefactions)

•

Interference

A number of different waves can add, constructively or destructively.

The superposition of two or more waves results in interference.

This is known as superposition.

Destructive Interference:

Exactly out of Phase

Cancellation + Zero

displacement

Constructive Interference:

In PhaseMaximum Displacement

Reinforcement

+

•

Interference Pattern

The pattern formed by superposition of different sets of waves that produce mutual reinforcement in some places and cancellation in others.

Superposition Principle of Wave

•

Standing Wave

A stationary wave pattern formed in a medium when two sets of identical waves pass through the medium in opposite directions.

lecture demos

Standing Wave

V

V

V

V

Standing Wave

Incident Wave

Reflected Wave

Beats

•

Sometimes, two waves with slightly different frequencies but the same

amplitude can form the phenomenon known as beats.

15.11 Beats

Blue colored wave + green colored wave ==> red colored wave. Two waves with same amplitudes but slightly different frequencies.

•

Doppler Effect

The shift in received frequency due to motion of a vibrating source toward or away from a receiver.

15.6 The Doppler Effect

•

Bow WaveThe V-shaped wave made by an object moving across a liquid surface at a speed greater than the wave speed.

(Since the source is moving faster than the wave speed, the wavefronts pile up.)

•

Shock WaveThe cone-shaped wave made by an object moving at supersonic speed through a fluid.

(Here, the source is moving faster than the wave speed, which is the speed of sound!!)

(Super-sonic speed)

•

Sonic Boom

The loud sound resulting from the incidence of a shock wave.

(This is the result of the pile up of many wave fronts which produces a sonic boom)

•

Sonic Boom

Piled up wave fronts produce a shock wave

Plane

•

Twice the speed of sound - Mach 2

Plane

2 units

1 unit

Wave front

The End of Chapter 19