WAVES Vibrations that carry energy from one place to another.
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Transcript of WAVES Vibrations that carry energy from one place to another.
WAVESWAVES
Vibrations that carry energy from one Vibrations that carry energy from one place to anotherplace to another
Types of WaveTypes of Wave
Mechanical. Examples: slinky, rope, water, Mechanical. Examples: slinky, rope, water, sound, & earthquakesound, & earthquake
Electromagnetic. Examples: light, radar, Electromagnetic. Examples: light, radar, microwaves, radio, & x-raysmicrowaves, radio, & x-rays
What Moves in a Wave?What Moves in a Wave?
Energy can be transported over long Energy can be transported over long distancesdistances
The medium in which the wave exists has The medium in which the wave exists has only limited movementonly limited movement
Example: Ocean swells from distant stormsExample: Ocean swells from distant storms
Path of each bit of water is ellipse
Periodic WavePeriodic Wave
Source is a continuous vibrationSource is a continuous vibration The vibration moves outwardThe vibration moves outward
Wave Basics - VocabularyWave Basics - Vocabulary
WavelengthWavelength is distance from crest to crest or is distance from crest to crest or trough to troughtrough to trough
AmplitudeAmplitude is maximum height of a crest or depth is maximum height of a crest or depth of a trough relative to equilibrium levelof a trough relative to equilibrium level
Frequency and PeriodFrequency and Period
FrequencyFrequency, f, is number of crests (waves) that pass , f, is number of crests (waves) that pass a given point per seconda given point per second
PeriodPeriod, T, is time for one full wave cycle to pass, T, is time for one full wave cycle to pass T = 1/f f = 1/T (inverses or reciprocals)T = 1/f f = 1/T (inverses or reciprocals) Waves /second = seconds/wave = Waves /second = seconds/wave = f T
Unit of FrequencyUnit of Frequency
Hertz (Hz)Hertz (Hz) SecondSecond-1 -1 same as 1/second or per secondsame as 1/second or per second Used to be “cycles per second”Used to be “cycles per second”
Wave VelocityWave Velocity
Wave velocity,v, is the velocity at which any part Wave velocity,v, is the velocity at which any part of the wave movesof the wave moves
If wavelength = If wavelength = v = v = ff Example: a wave has a wavelength of 10m and a Example: a wave has a wavelength of 10m and a
frequency of 3Hz (three crests pass per second.) frequency of 3Hz (three crests pass per second.) What is the velocity of the wave? Hint: Think of What is the velocity of the wave? Hint: Think of each full wave as a boxcar. What is the speed of each full wave as a boxcar. What is the speed of the train?the train?
v = v = f f v/f f = v/ v/f f = v/ lambdalambdawavelengthwavelength
f frequency f frequency
v is sometimes called v is sometimes called velocity velocity ofof propagation propagation (speed wave (speed wave moves in medium) moves in medium)
ExampleExample
A ocean wave travels from Hawaii at 10 A ocean wave travels from Hawaii at 10 meters/sec. Its frequency is 0.2 Hz. What meters/sec. Its frequency is 0.2 Hz. What is the wavelength?is the wavelength?
= v/f = 10/0.2 = 50 m
Second exampleSecond example
What is the wavelength of 100 MHz FM What is the wavelength of 100 MHz FM radio waves? Use v = c = 3 x 10radio waves? Use v = c = 3 x 1088 m/s m/s
= v/f = 3 x 10= v/f = 3 x 1088 m/s m/s ÷ 100 ÷ 100 x 10x 1066 s s-1-1
= (300 x 10= (300 x 1066)) ÷ (100 ÷ (100 x 10x 1066)) mm = 3.0 m= 3.0 m
Another exampleAnother example
Waves travel 75 m/s on a certain stretched Waves travel 75 m/s on a certain stretched rope. The distance between adjacent crests rope. The distance between adjacent crests is 5.0 m. Find the frequency and the period.is 5.0 m. Find the frequency and the period.
f = v/f = v/ f = 75 m/s f = 75 m/s ÷ 5.0 m = 15 Hz = 15 s÷ 5.0 m = 15 Hz = 15 s-1-1
T =T = 1/15 = 0.066666 s1/15 = 0.066666 s
Longitudinal vs. Transverse Longitudinal vs. Transverse WavesWaves
Transverse: particles of the medium move Transverse: particles of the medium move perpendicular to the motion of the waveperpendicular to the motion of the wave
Longitudinal: vibrations in same direction as waveLongitudinal: vibrations in same direction as wave
Longitudinal WaveLongitudinal Wave
Can be thought of as alternating Can be thought of as alternating compressionscompressions (squeezing) and expansions (squeezing) and expansions or or rarefactionsrarefactions (unsqueezing) (unsqueezing)
Sound Wave in AirSound Wave in Air
Compressions and rarefactions of air Compressions and rarefactions of air produced by a vibrating objectproduced by a vibrating object
Waves and EnergyWaves and Energy
Waves with large amplitude carry more Waves with large amplitude carry more energy than waves with small amplitudeenergy than waves with small amplitude
ResonanceResonance
Occurs when driving frequency is close to Occurs when driving frequency is close to natural frequency (all objects have natural natural frequency (all objects have natural frequencies at which they vibrate)frequencies at which they vibrate)
Tacoma Narrows bridge on the way to destruction– large amplitude oscillations in a windstorm
InterferenceInterference
Amplitudes of waves in the same place at Amplitudes of waves in the same place at the same time add algebraically (principle the same time add algebraically (principle of superposition)of superposition)
Constructive interference:Constructive interference:
Destructive InterferenceDestructive Interference
Equal amplitudes(complete):Equal amplitudes(complete):
Unequal Amplitudes(partial):Unequal Amplitudes(partial):
ReflectionReflection
Law of reflection:Law of reflection:
Angle of Incidence equals angle of Angle of Incidence equals angle of ReflectionReflection
Hard Reflection of a PulseHard Reflection of a Pulse
Reflected pulse is invertedReflected pulse is inverted
Soft Reflection of a PulseSoft Reflection of a Pulse
Reflected pulse not invertedReflected pulse not inverted
Standing WavesStanding Waves
Result from interference and reflection for Result from interference and reflection for the “right” frequencythe “right” frequency
Points of zero displacement - “nodes” (B)Points of zero displacement - “nodes” (B) Maximum displacement – antinodes (A)Maximum displacement – antinodes (A)
Formation of Standing WavesFormation of Standing Waves
Two waves moving in opposite directionsTwo waves moving in opposite directions
Examples of Standing WavesExamples of Standing Waves
Transverse waves on a slinkyTransverse waves on a slinky Strings of musical instrumentStrings of musical instrument Organ pipes and wind instrumentsOrgan pipes and wind instruments Water waves due to tidal actionWater waves due to tidal action
Standing Wave Patterns on a Standing Wave Patterns on a StringString
““Fundamental” = Fundamental” =
Wavelength vs. String LengthWavelength vs. String Length
Wavelengths of first 4 harmonicsWavelengths of first 4 harmonics
L
f =v
Frequencies are related by whole Frequencies are related by whole numbersnumbers
ExampleExample ff1 1 = 100 Hz fundamental= 100 Hz fundamental ff2 2 = 200 Hz 2= 200 Hz 2ndnd harmonic harmonic ff3 3 = 300 Hz 3= 300 Hz 3rdrd harmonic harmonic ff4 4 = 400 Hz 4= 400 Hz 4thth harmonic harmonic etcetc Other frequencies exist but their amplitudes Other frequencies exist but their amplitudes
diminish quickly by destructive interferencediminish quickly by destructive interference
Wave velocity on a stringWave velocity on a string
Related only to properties of mediumRelated only to properties of medium Does not depend on frequency of waveDoes not depend on frequency of wave vv2 2 = T/m/l Tension divided by mass per = T/m/l Tension divided by mass per
unit length of stringunit length of string
First Three Harmonics in Open First Three Harmonics in Open TubeTube
Amplitudes are largest at the open ends
Amplitudes zero at the nodes
BeatsBeats
Two waves of similar frequency interfereTwo waves of similar frequency interfere
Beat frequency equals the difference of the two interfering frequencies