WAVE MOTION

WHAT IS A WAVE?

A disturbance that transfers energy, not matter,

through space.

Pulse – a single disturbance moving through a

medium (a substance or material which carries a wave).

Wave – a repeating disturbance moving

through a medium.

THE ANATOMY OF A WAVE

Dashed line – the rest position, no disturbances

Crest – maximum upward displacement.

Trough – maximum downward displacement.

Amplitude – maximum displacement (height of wave); amount of energy a wave carries.

Wavelength – The distance between 2 successive points in phase.

A transverse wave

FREQUENCY & PERIOD

Frequency (symbol = f)

The number of complete vibrational cycles of a medium per a given amount of time.

i.e. cycles/second, waves/second, vibrations/second,

Units: Hertz (Hz)- cycles per second

Period (symbol = T)\

The time for a particle on a medium to make one complete vibrational cycle. Units: Second

T = 1 f = 1f T

PRACTICE

Ocean waves are timed to have traveled one

wave length in 3.44 s. What is the frequency of

the waves?

A car tire revolves with a frequency of 10 Hz.

How long does one revolution take?

TYPES OF WAVES

Transverse Waves

A wave that occurs when the medium (spring,

water, rope, etc.) moves or vibrates perpendicular

(90) to the direction of the wave motion.

TYPES OF WAVES

Longitudinal Waves

A wave in which particles of the medium move in a

direction parallel to the direction which the wave

moves.

TYPES OF WAVES

Surface Waves

A wave in which particles of the medium undergo

a circular motion. These waves are neither

longitudinal nor transverse.

TYPES OF LABS

3 types

Find a mathematical relationship

Determine a value

Test an already understood statement/law

For mathematical relationship labs, the objective

is always stated as:

Find the mathematical relationship between

_dependent_and _independent_ variables of the

object.

STEPS/REQUIREMENTS FOR M.R. LABS:

State your objective

First variable in statement is always the dependent (y-axis) variable

You will most likely measure this value, it is what you are testing

Second variable in statement is always the independent (x-axis) variable

You determine and control this variable

Collect your data in a chart

Graph your data, find the Line of Best Fit (LBF)

Use the LBF to determine the TE and MRS

TE –Translated Equation

MRS – Mathematical Relationship Statement

Translated Equation: stating the relationship of

the two variables in an equation for future

calculations and relating

Use the general form from your WS to help you

Mathematical Relationship Statement: a

written sentence that states how the variables

relate

Used to help describe with words

DETERMINING THE M.R. BETWEEN THE

WAVELENGTH AND FREQUENCY OF A WAVE

Objective:

Determine the mathematical relationship between

the wavelength of a wave and the frequency of that

wave.

WHAT IS THE MATHEMATICAL RELATIONSHIP

BETWEEN WAVELENGTH AND FREQUENCY?

Wavelength is inversely proportional to

frequency

Translated equation:𝑤𝑎𝑣𝑒𝑙𝑒𝑛𝑔𝑡ℎ =(𝑛𝑢𝑚𝑏𝑒𝑟)

𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦

What are the units for the constant in your TE?

m/s: This is speed!!!!!!

THE WAVE SPEED EQUATION

Speed = wavelength frequency

v = f(m/s) (m) (Hz = 1/s)

A sound wave has a frequency of 262 Hz and a wavelength measured at 1.29 m.

a) What is the speed of the wave?

b) How long will it take to travel the length of a 91.4-m football field.

c) What is the period of the wave?

FACTORS AFFECTING WAVE SPEED

Remember…. Speed = distance/time

Speed of a Wave

TrialTension

(N)

Frequency

(Hz)

Wavelength

(m)

Speed

(m/s)

1 2.0 4.05 4.00 16.2

2 2.0 8.03 2.00 16.1

3 2.0 12.30 1.33 16.4

4 2.0 16.2 1.00 16.2

5 2.0 20.2 0.800 16.2

6 5.0 12.8 2.00 25.6

7 5.0 19.3 1.33 25.7

8 5.0 25.5 1.00 25.5

FACTORS AFFECTING WAVE SPEED

The speed of a wave does not depend on the

amplitude (height/energy) of the wave.

The speed of a wave does depend on the

medium through which the wave is moving.

BEHAVIOR OF WAVES

Wave Interference

The phenomenon which occurs when 2 waves meet while traveling along the same medium.

Principle of superposition

When 2 waves interfere, they combine to form a new wave, which is the algebraic sum of the displacements of the individual waves at the same location. The waves continue to pass through one another after the interference.

BEHAVIOR OF WAVES, CONTINUED…

Constructive Interference

Occurs when interfering waves have displacements in the same direction. crest – crest trough – trough

Amplitudes add

BEHAVIOR OF WAVES, CONTINUED…

Destructive Interference

Occurs when interfering waves have

displacements in the opposite direction.

crest – trough

Amplitudes subtract

BEHAVIOR OF WAVES, CONTINUED…

Two Source Interference Twin water bugs Jimminy and Johnny are both creating a series of circular waves by jiggling their legs in the water. The waves undergo interference and create the pattern represented in the diagram at the left. The thick lines in the diagram represent wave crests and the thin lines represent wave troughs. Several of positions in the water are labeled with a letter. Categorize each labeled position as being a position where either constructive or destructive interference occurs.

A crest of amplitude 6 cm meets an opposing

crest of amplitude 4 cm. What is the amplitude

when the two waves interfere? Draw the resulting

wave diagram.

BEHAVIOR OF WAVES, CONTINUED…

A crest of amplitude 11 cm meets an opposing

trough of amplitude 8 cm. What is the amplitude

when the two waves interfere? Draw the resulting

wave diagram.

BEHAVIOR OF WAVES, CONTINUED…

BEHAVIOR OF WAVES, CONTINUED…

Reflection

When waves reach a

barrier they bounce

off and head in a

different direction.

The angle at which the

waves approach the

barrier will always

equal the angle at

which they reflect off

the barrier.

BEHAVIOR OF WAVES, CONTINUED…

Refraction

Involves a change in

direction of the

waves as they pass

from one medium to

another.

As the wave bends,

a change in speed

and wavelength also

occurs.

BEHAVIOR OF WAVES, CONTINUED…

Diffraction

Involves a change in

direction of waves as

they pass through an

opening or around a

barrier in their path.

i.e., waves in a harbor

bend around boats or

hearing someone

speaking from an

adjacent room.

THE NATURE OF A SOUND WAVE

Sound is a wave that is created by a vibrating

source that creates disturbances in surrounding

air molecules.

Sound needs a medium to travel from one location

to another, thus it is a mechanical wave.

For sound traveling through air, the vibrations of

the particles are best described as longitudinal.

THE NATURE OF A SOUND WAVE, CONTINUED…

Because of the

longitudinal motion of

the air particles, there

are regions in the air

where air particles are

compressed together

(compressions) and

other regions where the

air particles are spread

apart (rarefactions).

BEHAVIOR OF SOUND WAVES

Constructive interference occurs when either 2

compressions or 2 rarefactions meet. If there is

continuous reinforcement a very loud sound is

produced (antinodes).

Destructive interference occurs when

compressions meet rarefactions. If there is

continuous canceling, no sound will be heard

(nodes).

BEHAVIOR OF SOUND WAVES, CONTINUED

Two Source Sound

InterferenceThick lines = compressions

Thin line = rarefactions

SOUND PROPERTIES

As sound moves through a medium, each particle of the medium vibrates at the same frequency.

Pitch – the sensation of frequencies high pitch = high frequency low pitch = low frequency

Intensity – the amount of energy transported large amplitude = high intensity (louder*) small amplitude = low intensity (softer*)

* The loudness of a sound is subjective. The same sound will not be perceived to have the same loudness to all individuals.

VOLUME

Intensity is the amount of energy transported past a given area of medium per unit of time

Intensity = Energy /(time * area) or (since Power=Energy/time)…

Intensity = Power/ Area

Volume is based on a logarithmic scale of base 10 in intesity

Volume is measured in Decibels

0 Decibels (dB) is considered the “Threshold of Hearing”

VOLUME EXAMPLESSource Intensity IntensityLevel # of TimesGreater Than TOH

Threshold of Hearing (TOH) 1*10-12 W/m2 0 dB 100

Rustling Leaves 1*10-11 W/m2 10 dB 101

Whisper 1*10-10 W/m2 20 dB 102

Normal Conversation 1*10-6 W/m2 60 dB 106

Busy Street Traffic 1*10-5 W/m2 70 dB 107

Vacuum Cleaner 1*10-4 W/m2 80 dB 108

Large Orchestra 6.3*10-3 W/m2 98 dB 109.8

Walkman at Maximum Level 1*10-2 W/m2 100 dB 1010

Front Rows of Rock Concert 1*10-1 W/m2 110 dB 1011

Threshold of Pain 1*101 W/m2 130 dB 1013

Military Jet Takeoff 1*102 W/m2 140 dB 1014

Instant Perforation of

Eardrum1*104 W/m2 160 dB 1016

THE SPEED OF SOUND

Speed = distance/time

v = x / t

A tuning fork produces a sound wave in air with

a frequency of 261.6 Hz. At room temperature

the speed of sound is 343 m/s. What is the

wavelength?

FACTOR AFFECTING WAVE SPEED

Remember… the speed of any wave depends upon

the properties of the medium through which the

wave is traveling.

Looking at the elastic properties (maintaining

shape) and the inertial properties the following

pattern can be observed:

vsolids > vliquids > vgases

Sound travels slower in cool air than in warm air.

BEHAVIOR OF SOUND WAVES

Resonance

Occurs when one object vibrating at the same natural frequency of a second object forces the second object into vibrational motion.

The result of resonance is always a big vibration –a loud sound!

Resonance is the cause of sound production in musical instruments.

DOPPLER EFFECT

Occurs whenever the source of waves is moving with respect to an observer.

There is an apparent upward shift (higher frequency = higher pitch) for observers whom the source is approaching.

There is an apparent downward shift (lower frequency = lower pitch) for observers whom the source is receding.

DOPPLER EFFECT, CONTINUED…

The actual frequency does not change!

STANDING WAVES

A pattern that results when a wave is confined to a given space in a medium.

The wave pattern is only produced when one end of the rope is vibrated at just the right frequency.

Nodes – areas of no displacement

(destructive interference)

Antinodes – areas of maximum displacement

(constructive interference)

STANDING WAVES, CONTINUED…

1st

Harmonic

2nd

Harmonic

3rd

Harmonic

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f:

v:

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f:

v:

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f:

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