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Definition Wave:Any transfer of energy without a transfer of matter Wave Pulse: the disturbance that transfers energy Periodic Wave: a series of identical, repeating evenly spaced pulses

Medium: The substance through which waves pass or propagate Transverse Wave: A wave in which a medium moves perpendicular to the direction of wave propagation Longitudinal Wave: A wave in which a medium moves parallel to the direction of wave propagation

Vibrations & Waves ntro_wave_phenomena.htm

Longitudinal wave Condensations: areas of maximum compressions; analogous to crests Rarefactions: areas of maximum separation; analogous to troughs.

Vibrations & Waves Wavelength - Distance between peaks Amplitude - Max Height above resting spot Related to the energy carried by the wave Corresponds to loudness in sound waves and brightness in light waves Frequency - Number of Bounces/second Period - Time of a complete vibration Period = 1 / FrequencyT = 1/f Frequency = 1 / Period

Waves can be produced in two ways: a. Vibration of particles - this requires a medium for transfer (mechanical wave) ex) sound, water wave, spring wave b. Small changes in the strength of an electromagnetic field - this requires no medium for transfer ex) light, microwaves, x-rays

Pulses & Periodic Waves 1. Pulse – single vibratory disturbance that moves from point to point (Medium only moves up and down) Ex)In which direction will segment X move as the wave passes through it? (1) down, only (2) up, only (3) down, then up, then down (4) up, then down, then up

Pulses & Periodic Waves 1. Pulse – single vibratory disturbance that moves from point to point (Medium only moves up and down) Ex)In which direction will segment X move as the wave passes through it? (1) down, only (2) up, only (3) down, then up, then down (4) up, then down, then up

a.When the pulse (wave) reaches a boundary with another medium, part is reflected and part is transmitted (goes through) From high speed to low speed (low density to high density) From low speed to high speed (high density to low density)

Reflection from a rigid boundary (reflected wave undergoes a 180 o phase change) Reflection from a free boundary reflected wave has the same polarity (no phase change) as the incident wave b. When a pulse reaches a fixed, unyielding boundary, then the pulse is completely reflected and inverted (180°)

Wave characteristics mations3/waves/Wave_Characteristics.html mations3/waves/Wave_Characteristics.html mations3/waves/waves2.html mations3/waves/waves2.html

Frequency example Ex) A wave generator operating for 4 seconds produces the waves drawn below. Top view of a periodic wave (Each line is a crest) How many waves are drawn between A and B? (Be careful!!) 8 cycles

example Ex) A wave generator operating for 4 seconds produces the waves drawn below. Top view of a periodic wave (Each line is a crest) What is the frequency of this periodic wave train? f = 8 cycles/4 sec = 2 cycles/sec = 2 Hz

Frequency In Sound, frequency is pitch. -Human Ear: Frequency Range 20 Hz - 20,000 Hz. hill.com/sites/ /student_view0/chapter19/ani mation__effect_of_sound_waves_on_cochlear_structure s__quiz_2_.html In Light, frequency is color.

Period T = 1/f Period (seconds) – time for an entire wave cycle to pass a given point in a medium - determined by source of vibration not medium Ex) The frequency of a light wave is 5.0 x hertz. What is the period of the wave? T = 1/f = 1/(5.0 x hertz) = 2.0 x s

Which has the largest period? B (will take the longest to pass by)

Amplitude Amplitude – maximum change in position of a particle from its rest position during a single vibration - determined by source of vibration, not medium Amplitude of a wave shows the amount of energy in the wave Amplitude is a measure of loudness for sound and brightness for color -

Phase "In Phase" (0°) – points on a single periodic wave that have the same displacement (from equilibrium position) and moving in the same direction Whole number of wavelengths apart A & E, A & I, A & M B & F, B & J, B & N

Phase "Out of Phase"– (180 0 ) - same displacement from equilibrium position but going in a different direction ½, 1½, 2½ etc wavelengths apart A & C, B & D, F & H

Which 2 points are in phase? C and F Name 2 points that are 180° out of phase? B and DE and G

Wavelengthλ Wavelength – distance between two consecutive points in phase determined by medium λ = length of one cycle in meters / # of cycles

Ex) Wavelength? λ = 5.0 m/2.5 cycles λ = 2.0 m

Ex) Amplitude? Wavelength? Amplitude =.10 m Wavelength =.60 m

Ex)Amplitude A?, B?, C? Amplitude of A = 2.0 m Amplitude of B = 2.0 m Amplitude of C = 1.0 m

Speed: v = f λ Speed – the number of meters a single cycle travels per second Speed of wave depends on the medium (slower in dense media) w/outsideContent/waves/speedMechanical_wave.htm

Speed: v = f λ Speed – the number of meters a single cycle travels per second Solve for f : f = v / λ Frequency and Wavelength are INVERSELY RELATED

Ex) f = 40. hertz. V = ? (1) 13 m/s (2) 27 m/s (3) 60. m/s (4) 120 m/s V = fλ V = 40. Hz(1.5 m) (3) 60. m/s

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Velocity Velocity sound = 3.3 x 10 2 m/s (Air, Reference Table, room temperature) Velocity light in a vacuum = 3 x 10 8 m/s About how many times faster is light than sound? About 1 million times

Speed of Sound Depends on the material of the vibrating medium Sound can vibrate water, wood (speaker enclosures, pianos), metal, plastic, etc. Sound speed in dry air is 330 meters/second at 0 o C Faster in warm air, slower in cold Water 4 times faster, steel 15 times faster

Summary SourceMedium FrequencySpeed PeriodWavelength Amplitude

Doppler Effect effect.html effect.html Sheldon explains: tions3/waves/DopplerEffectTrain.html tions3/waves/DopplerEffectTrain.html

Doppler Effect Doppler Effect – variation in the observed frequency of a wave when there is relative motion between the source of the wave and the receiver Because car is “driving into it’s sound wave” the observer in front of car hears a higher frequency. An observer behind the car hears a lower frequency.

Which way is the source of this wave moving? To the right, where the frequency is higher

Doppler effect on electromagnetic waves For Electromagnetic waves, such as visible light, the frequency change is recorded as a color shift. Astrophysicist site this phenomenon as proof that universe is expanding.

Sonic Boom Or - What happens when you go faster than the speed of sound m/ m/ Interesting Fact: The crack of a whip is the sound of the tip breaking the speed of sound.

Wave Front – locus of adjacent points on a wave which are in phase Top View

Superposition Superposition – when waves overlap, the resultant displacement is the algebraic sum of the individual displacements of each wave – This causes interference sics%20B%20II/course%20files/multimedia/lesson42/ lessonp.html sics%20B%20II/course%20files/multimedia/lesson42/ lessonp.html

Interference – effect produced by two waves passing simultaneously through a region There exist two kinds of interference: 1. Constructive interference 2. Destructive interference sics%20B%20II/course%20files/multimedia/lesson46/ lessonp.html sics%20B%20II/course%20files/multimedia/lesson46/ lessonp.html

Example As the two waves below pass through each other, the medium at point P will … (1) vibrate up and down (2) vibrate left and right (3) vibrate into and out of the page (4) remain stationary June 2004

Example As the two waves below pass through each other, the medium at point P will … (1) vibrate up and down (2) vibrate left and right (3) vibrate into and out of the page (4) remain stationary June 2004

Example What will the amplitude of the resultant wave be when wave A and B meet at point X? Amp A + Amp B = = +1

One more ex (6/09) What is the amplitude of the wave produced when these waves overlap? 15 cm

Symmetrical Lines of Interference mations3/waves/interference.swf mations3/waves/interference.swf wave patterns produced by the overlap of 2 wave fronts in phase Maximum Constructive Interference – Phase difference – whole wavelength Maximum Destructive Interference - Phase Difference - 1/2 wavelength interference/videos/632-mit-physics-demo---- microwave-interference interference/videos/632-mit-physics-demo---- microwave-interference

Ex) What kind of interference occurs at point P? Destructive Interference

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Standing Waves mations3/standingWaves.swf mations3/standingWaves.swf Standing Wave – waves produced when two waves of the same frequency and amplitude travel in opposite directions in the same medium (ex. Musical instruments) #docid=

definitions Antinode – The point of maximum displacement of a medium Node – Regions of zero displacement of the medium. Caused by maximum destructive interference Standing waves can also be created by reflection

ex How many Nodes? 5 How many antinodes? 4 How many waves? 2

Harmonics

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Periodic Wave Phenomena Beats and resonance forks-resonance-a-beat-frequency / forks-resonance-a-beat-frequency /

Beats Occur when two sound waves of nearly the same frequencies (ex. 256Hz and 258 Hz) interact with one another Beat Freq: Larger freq – smaller freq Pitch of resulting soundwave is the average of the two freq. In our example f 1 = 256 Hzf 2 = 258 Hz Beat Frequency : f 2 - f 1 = 258 Hz – 256 Hz = 2 beats / sec Pitch = avg. freq = f 2 + f 1 = 258 Hz Hz = 257 Hz 22

Resonance When the forced vibration matches a natural frequency we get a “resonance” condition Think about a swing on a playground You go high when you pump the swing at its natural vibration frequency Sympathetic vibrations in tuning forks Famous Tacoma Narrows bridge collapse narrows-bridge-video.htm narrows-bridge-video.htm

Resonance Resonance – Building up of energy by adding small amounts of energy in time with the natural frequency of an object

Resonance Frequency Resonance Frequency – natural frequency that an object vibrates when disturbed Can sound be used to break glass? Great video! with-sound with-sound

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Diffraction – the spreading out of a wave into the region behind an obstacle Amount of Diffraction depends on Wavelength & Size of Slit. Diffraction increases when size of the slit approaches wavelength size. ghschool/physics/home/n otes/waves/WaveBehavior /diffractionSlitD.swf ghschool/physics/home/n otes/waves/WaveBehavior /diffractionSlitD.swf

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Wave Reflection When a sound wave reflects from a surface we generate an echo Wave reflection from surfaces depends on the characteristics of the surface Smooth hard surfaces reflect best Rough soft surfaces reflect poorly Energy not reflected is absorbed or transmitted through the material

Wave Reflection Think of arrows pointing in the direction of the wave motion We can trace the path of these arrows Angle of incidence = Angle of reflection (θ 1 =θ 2 ) Angles Equal

Wave Reflection Acoustics of room design is very interesting. Need some reflections to “liven” the room. Too many reflections and the sound gets mushy. Look in a concert hall or auditorium to see the different sound treatments

Wave Refraction If there is a change in the characteristics of a medium, waves are bent This occurs because different parts of the wave front travel at different speeds Think of a marching around a curved track The inside people have to move more slowly than the outside people to keep the lines straight

Wave Refraction

Wave Reflection & Refraction The combination of reflection and refraction enables imaging Ultrasonic medical imaging Naval SONAR for detecting submarines Bats catch mosquitoes