Waves

Waves

Definition of wave

– A disturbance that transfers energy through matter or space

– “Disturbance”-a change from a normal state

Periodic or Harmonic Motion

Motion that repeats itself in the same amount of time

One repetition of motion called a cycle

Examples? What does graph look

like?

Amount of time to complete cycle called a period (T)

Frequency (f) is how many complete cycles occur in one second

T = 1/f or f =1/T Amplitude is the amount

of displacement from rest

Periodic or Harmonic Motion

Graphing harmonic motion

http://www.mcanv.com/pend1.html

Graphing Harmonic Motion

http://www.gailruby.com/Picture4.png

http://en.wikipedia.org/wiki/File:Simple_harmonic_oscillator.gif

Homework

Complete Harmonic Motion Worksheet

Waves demonstrate harmonic motion

Wave movement through matter– Particles move– Particles return to original position (location)

http://upload.wikimedia.org/wikipedia/commons/7/74/Simple_harmonic_motion_animation.gif

Types of Waves

Based on particle motion in wave

2 types1. Transverse

2. Longitudinal

Wave Type-Transverse

Particle motion perpendicular to wave direction

http://upload.wikimedia.org/wikipedia/commons/6/6d/Onde_cisaillement_impulsion_1d_30_petit.gif

Wave Type-Transverse

Particle motion perpendicular to wave direction

http://www.kettering.edu/~drussell/Demos/waves-intro/waves-intro.html

Parts of a Transverse Wave

http://library.thinkquest.org/15433/unit5/transv1.gif

Examples of Transverse Waves

Shaking a string Ocean waves Ripples on a pond “Stadium” or human wave Electromagnetic (radio, light, micro ect…)

Wave Type-Longitudinal

Particle motion in direction of wave

http://en.wikipedia.org/wiki/Image:Onde_compression_impulsion_1d_30_petit.gif

Wave Type-Longitudinal

Particle motion in direction of wave

Parts of a Longitudinal Wave

Particle motion in direction of wave

Examples of Longitudinal Waves

Sound waves Oscillating springs

Sound waves are longitudinal waves

http://emusictips.com/wp-content/uploads/2009/03/sound_waves_animated.gif

Represent longitudinal waves as transverse waves

Particle displacement in a longitudinal wave can be graphed as a transverse wave– Particle motion from rest graphed as amplitude

http://faraday.physics.utoronto.ca/IYearLab/Intros/StandingWaves/Flash/long_wave.html

Sound Waves

Sound waves move vibrational energy through matter

Sound waves are longitudinal waves

Wave Properties

Common Characteristics of Wave– Length– Height– Frequency (how often they occur)

Period (how long to make 1 cycle)– Speed

All Characteristics of Waves Can Vary

Wave Characteristics

Wavelength (λ)-the distance between repeating parts of a wave– Trough to trough– Peak to Peak– Rarefaction to

Rarefaction – Compression to

compression- Or any other

repeating part

Wave Characteristics

Wave amplitude (height)-the maximum displacement from the undisturbed position of the medium to the top of a crest or bottom of a trough

Check Your UnderstandingTransverse Waves

The wavelength of the wave in the diagram above is given by letter ______.

The amplitude of the wave in the diagram above is given by letter _____.

Check Your UnderstandingTransverse Waves

Indicate the interval which represents one full wavelength.

Wave Characteristics

The frequency (f) of a wave is the number of complete waves (cycles) that pass the observer in a given time.

Hertz is the unit of frequency, and just means how many cycles (peaks) per second.

Wave Characteristics

The period (T) of a wave is the time for a wave to make one complete cycle (peak to peak).

The period is related to the frequency by the following equation f=1/T

Wave Characteristics

The speed (v) of a wave is the how fast the wave is moving– distance the wave travels in a certain amount of

time.

Wave Characteristics

The relationship between the speed, frequency, period and wavelength

Example:– 2 waves each second (i.e. frequency = 2 Hz)– the period is equal to 1/f = ½ second– the distance between the waves as 25 cm: this is the

wavelength. In 0.5 s, waves move 25 cm, so we can find the

speed using: speed= v = λ x f = 25 x 2 = 50 cm/sec OR speed = v = λ x 1/T = 25 x (1÷ ½) = 50

cm/sec

Homework

Complete Wave Worksheet

Factors Affecting the Speed of Sound

Sound waves require matter to travel– No particles to compress = no waves = no sound

Speed of sound depends on matter or medium– Speed does not depend of the source

Factors that affect the speed of sound include:– Temperature of medium– Elasticity of medium– Density of medium

Speed of Sound

Temperature Affects– Temperature changes affect sound speed more in

gases than solids or liquids Particles spaced apart in gases Temperature affects spacing of particles in gases

(Charles & Boyles Gas Laws) Temperature

– High temperature air = higher sound speed– Low temperature air = lower sound speed– Heat and sound = kinetic energy

Speed of Sound

Elasticity– Elasticity = The tendency of an object to return to

its original shape once the forces are no longer applied.

– Phases of matter have great effect on elasticity of matter

– Greater elasticity = Greater speed of sound– vsolids > vliquids > vgases

Speed of Sound

Density – Less effect on speed of sound than elasticity– Within a single phase of matter = greater impact– Density = mass/volume– Within a single phase of matter

Greater density = lower speed of sound Mass of heavier particles are harder to move Greater density = Greater inertia

Speed of Sound

Materials– The speed of sound

varies through different materials

Material Speed of Sound (m/s)

Iron 5890

Lead 1960

Water 1479

Ice 3980

Air 330

Sonic Boom

When an object travels faster than the speed of sound it breaks the “sound barrier”

Waves all traveling at same speed, pile up on each other as plane pushes them together

Result is a “sonic boom”

Properties of Sound

Intensity-measure of sound’s amplitude– Related to loudness,

but loudness is subjective

Intensity measured in decibels (dB)

Increase in 10 dB results in sound that is twice as loud

Source Intensity Level (dB)

Threshold of hearing (TOH) 0

Rustling leaves 10

Whisper 20

Normal conversation 60

Busy street traffic 70

Vacuum cleaner 80

Rock concert 110

Threshold of pain 130

Military jet takeoff 140

Eardrum perforation 160

Properties of Sound

Frequency and Pitch– Frequency is number of waves in a certain amount of time– Frequency is measured in Hertz (Hz)– Pitch is related to frequency, describes how high or low the

sound is. Pitch is subjective.– Pitch is the sensation of frequencies

High frequency = high pitched sounds

Low frequency = low pitched sounds

Human Hearing and Frequency

Humans can hear frequencies ranging from 20-20,000 Hz

Ultrasound are sound waves with frequencies above the human hearing range

Properties of Sound

Sound Quality is referred to Timbre Differences in timbre allow listeners to hear

not only the difference between an oboe and a flute, but also the difference between two different flutes, even if both flutes are playing notes at the same frequency and amplitude

Properties of Sound

Descriptions related to timbre– Reedy – Brassy – Clear – Rounded – Piercing – Strident – Harsh

– Warm – Mellow – Resonant – Dark or Bright – Heavy or Light – Flat – Having much, little,

or no vibrato

Properties of Sound

Doppler Effect The observed effect

between an observer and a sound source when one is moving relative to another– distance decreasing →

perceived frequency (pitch) is increased

– distance increasing → perceived frequency (pitch) is decreased

http://imagine.gsfc.nasa.gov/YBA/M31-velocity/Doppler-shift-2.html

Doppler Effect

Examples– http://www.lon-capa.org/~mmp/applist/doppler/d.h

tm (visual)

– http://galileoandeinstein.physics.virginia.edu/more_stuff/flashlets/doppler.htm

(visual and audio)

Wave Interactions

What is the result of collisions between waves and other waves or objects?– Waves transfer energy– Collisions results in energy transfer

Lose or gain energy

Wave Interactions

Wave colliding with other waves cause interference– Principle of Superposition

Waves add (subtract) amplitudes (energy)– Two kinds of interference

Constructive (add) Destructive (subtract)

Sound Wave Interactions

Interference– Constructive =

increase in intensity

– Destructive = decrease in intensity

Wave Interactions

Constructive Interference– waves add to produce a new wave with larger peaks than

either of the two original waves

Wave Interactions

Constructive interference

Wave Interactions

Destructive Interference– waves add to produce a new wave with smaller peaks

than either of the two original waves

Sound Wave Interactions

Interference

Phase shifts of waves

The phase shift tells an observer how out of sync two or more waves are– It gives the offset

of the two waves

In phase = constructive interferenceOut of phase = destructive interference

In phase and out of phase waves

Waves are completely out of phase – destructive interference

Waves are completely in phase – constructive interference

Sonic Boom

Constructive interference of waves = sonic boom

Crack of a bull whip = sonic boom

Standing waves on a string

Harmonics ofStanding Waves

Harmonics of standing waves

http://www.magneticsolutions.com.au/images/harmonics.png

Homework

Complete Sound and Standing Waves Worksheets

Sound Wave Interactions

Resonance– Is the vibration of an

object at its natural frequency

This frequency depends on the length of the object

Sound Wave Interactions

Resonance– Tuning forks and bells vibrate at their natural

frequency All objects have a frequency that they resonate at

– When waves bounce back and forth on themselves within the object and constructively interfere, we call it resonance.

Sound Wave Interactions

Resonance Examples http://www.colorado.edu/physics/2000/micro

waves/standing_wave2.html http://en.wikipedia.org/wiki/Image:Tacoma_N

arrows_Bridge_destruction.ogg (Movie of Tacoma Narrows Bridge)

Wave Interactions

Wave colliding with objects have following 3 outcomes

1. Refraction

2. Reflection

3. Diffraction

Wave Interactions

REFLECTION– Reflection is when waves

bounce from a surface back toward the source.

– A mirror reflects the image of the observer.

– None of the characteristics of a wave are changed by reflection.

– No change-wavelength, frequency, period

– Change-wave direction

Wave Interactions

REFLECTION– Law of Reflection– Angle of Incidence =

Angle of Reflection

Sound Wave Interactions

Reflection– When a sound wave in air

reaches the surface of another material, some of the sound is reflected off the surface and some passes into the material (transmitted)

Sound Wave Interactions

Reflection– Smooth surfaces best

more sound will be reflected from a smooth wall made of mud than a pile of dirt

reason is that the rough or porous surface allows for many reflections, resulting in more absorption and less reflection

Sound Wave Interactions

Reflections– Echoes

When sound reflects off a smooth flat surface, an echo or reproduction of the sound can be heard.

Echoes are more noticeable if the surface is far enough away to allow for a time-lag between when the sound is made and when it is hear. (~0.1 seconds)

Echo Problem

If the speed of sound in air is 340 m/sec and you hear an echo 1 sec after you yell, how far away is the reflector?

Remember that that the sound wave has to travel there and back so V=total distance/time

340m/sec= total distance/1 sec

Total distance = 340 m/sec x 1 sec

= 340 m

Distance to reflector = total distance ÷ 2

= 170 m

Wave Interactions

DIFFRACTION– Diffraction is the

bending of waves when they collide with the edges of objects.

– All waves diffract.– We can hear around a

corner because of the diffraction of sound waves.

Sound Wave Interactions

Diffraction– Because sound waves diffract, you can

hear around corners and from behind obstacles

Wave Interactions

REFRACTION– Refraction is when

waves are deflected when passing from one medium to another

– The wave generally changes direction.

Sound Wave Interactions

Refraction is the bending of waves when they enter a medium where their speed is different.

Sound Wave Interactions

Refraction-Effect– Cool air-lower speed, Warm air-higher speed

Normally, only the direct sound is received. But refraction can add some additional sound, effectively amplifying the sound. Natural amplifiers can occur over cool lakes.

Homework

Complete Wave Interactions Worksheet

The End

http://therealstorie.files.wordpress.com/2008/06/lighthouse_waves_z.jpg