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Waves
Definition of wave
– A disturbance that transfers energy through matter or space
– “Disturbance”-a change from a normal state
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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?
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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
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Graphing harmonic motion
http://www.mcanv.com/pend1.html
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Graphing Harmonic Motion
http://www.gailruby.com/Picture4.png
http://en.wikipedia.org/wiki/File:Simple_harmonic_oscillator.gif
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Homework
Complete Harmonic Motion Worksheet
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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
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Types of Waves
Based on particle motion in wave
2 types1. Transverse
2. Longitudinal
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Wave Type-Transverse
Particle motion perpendicular to wave direction
http://upload.wikimedia.org/wikipedia/commons/6/6d/Onde_cisaillement_impulsion_1d_30_petit.gif
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Wave Type-Transverse
Particle motion perpendicular to wave direction
http://www.kettering.edu/~drussell/Demos/waves-intro/waves-intro.html
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Parts of a Transverse Wave
http://library.thinkquest.org/15433/unit5/transv1.gif
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Examples of Transverse Waves
Shaking a string Ocean waves Ripples on a pond “Stadium” or human wave Electromagnetic (radio, light, micro ect…)
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Wave Type-Longitudinal
Particle motion in direction of wave
http://en.wikipedia.org/wiki/Image:Onde_compression_impulsion_1d_30_petit.gif
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Wave Type-Longitudinal
Particle motion in direction of wave
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Parts of a Longitudinal Wave
Particle motion in direction of wave
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Examples of Longitudinal Waves
Sound waves Oscillating springs
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Sound waves are longitudinal waves
http://emusictips.com/wp-content/uploads/2009/03/sound_waves_animated.gif
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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
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Sound Waves
Sound waves move vibrational energy through matter
Sound waves are longitudinal waves
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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
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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
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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
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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 _____.
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Check Your UnderstandingTransverse Waves
Indicate the interval which represents one full wavelength.
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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.
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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
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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.
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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
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Homework
Complete Wave Worksheet
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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
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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
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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
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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
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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
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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”
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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
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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
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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
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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
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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
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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
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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)
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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
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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)
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Sound Wave Interactions
Interference– Constructive =
increase in intensity
– Destructive = decrease in intensity
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Wave Interactions
Constructive Interference– waves add to produce a new wave with larger peaks than
either of the two original waves
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Wave Interactions
Constructive interference
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Wave Interactions
Destructive Interference– waves add to produce a new wave with smaller peaks
than either of the two original waves
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Sound Wave Interactions
Interference
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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
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In phase and out of phase waves
Waves are completely out of phase – destructive interference
Waves are completely in phase – constructive interference
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Sonic Boom
Constructive interference of waves = sonic boom
Crack of a bull whip = sonic boom
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Standing waves on a string
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Harmonics ofStanding Waves
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Harmonics of standing waves
http://www.magneticsolutions.com.au/images/harmonics.png
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Homework
Complete Sound and Standing Waves Worksheets
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Sound Wave Interactions
Resonance– Is the vibration of an
object at its natural frequency
This frequency depends on the length of the object
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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.
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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)
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Wave Interactions
Wave colliding with objects have following 3 outcomes
1. Refraction
2. Reflection
3. Diffraction
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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
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Wave Interactions
REFLECTION– Law of Reflection– Angle of Incidence =
Angle of Reflection
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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)
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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
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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)
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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
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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.
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Sound Wave Interactions
Diffraction– Because sound waves diffract, you can
hear around corners and from behind obstacles
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Wave Interactions
REFRACTION– Refraction is when
waves are deflected when passing from one medium to another
– The wave generally changes direction.
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Sound Wave Interactions
Refraction is the bending of waves when they enter a medium where their speed is different.
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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.
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Homework
Complete Wave Interactions Worksheet
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The End
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