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Waves Types, characteristics, properties. Wave: definition A quantity or disturbance that changes in magnitude with respect to time at a given location.

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Presentation on theme: "Waves Types, characteristics, properties. Wave: definition A quantity or disturbance that changes in magnitude with respect to time at a given location."— Presentation transcript:

1 Waves Types, characteristics, properties

2 Wave: definition A quantity or disturbance that changes in magnitude with respect to time at a given location A quantity or disturbance that changes in magnitude with respect to time at a given location Also changes in magnitude from place to place at a given time Also changes in magnitude from place to place at a given time Propagates through a medium or space Propagates through a medium or space Transfers energy, not matter Transfers energy, not matter water wave, sound, light, x-ray, earthquake water wave, sound, light, x-ray, earthquake

3 Wave Classification Schemes Is medium needed for propagation? Mechanical Mechanical Electromagnetic Electromagnetic How do particles move compared to motion of wavefront? Transverse Longitudinal

4 Mechanical Waves Require elastic medium for propagation Require elastic medium for propagation Energy source vibrates particles of medium about an equilibrium position Energy source vibrates particles of medium about an equilibrium position Each particle exerts force on adjacent particles passing energy along Each particle exerts force on adjacent particles passing energy along Inertia of particles slows propagation of wave: wave speed depends on medium Inertia of particles slows propagation of wave: wave speed depends on medium

5 Mechanical Waves Particles move in SHM if wave train is generated by periodic motion Particles move in SHM if wave train is generated by periodic motion Examples: water waves, sound waves, earthquake waves, vibrating strings Examples: water waves, sound waves, earthquake waves, vibrating strings

6 Electromagnetic Waves Self-propagating--need no medium for propagation Self-propagating--need no medium for propagation Can travel through vacuum of space Can travel through vacuum of space Examples: light waves, microwaves, x-rays, radio & TV broadcasts Examples: light waves, microwaves, x-rays, radio & TV broadcasts

7 Transverse Waves Displacement of particles is perpendicular to direction of wave travel Displacement of particles is perpendicular to direction of wave travel crest: point of max. positive displacement crest: point of max. positive displacement trough: point of max. negative displacement trough: point of max. negative displacement examples: water, light, string, all electromagnetic waves examples: water, light, string, all electromagnetic waves

8 Longitudinal Waves Displacement of particles is parallel to direction of wave travel Displacement of particles is parallel to direction of wave travel Series of high and low pressure areas in medium Series of high and low pressure areas in medium Compression: high pressure area (like crest) Compression: high pressure area (like crest) Rarefaction: low pressure area (like trough) Rarefaction: low pressure area (like trough) Ex: sound, Slinky, some earthquake waves Ex: sound, Slinky, some earthquake waves

9 Characteristics of All Waves Energy: waves transport energy Energy: waves transport energy Phase: relative position between waves Phase: relative position between waves Frequency: how many waves per second Frequency: how many waves per second Period: how long a time for one wave Period: how long a time for one wave Wavelength: distance between waves Wavelength: distance between waves Speed: how fast wave travels Speed: how fast wave travels Amplitude: how big the wave is Amplitude: how big the wave is

10 Wave Energy Depends on amplitude, frequency, and density of medium Depends on amplitude, frequency, and density of medium Power (energy/time) is proportional to square of amplitude and/or frequency Power (energy/time) is proportional to square of amplitude and/or frequency With no losses to system, each wave has same energy as source With no losses to system, each wave has same energy as source As wave moves outward, energy spreads over larger area, reducing amplitude As wave moves outward, energy spreads over larger area, reducing amplitude

11 Phase In phase: waves (or particles) are moving together, peaks line up with peaks and troughs line up with troughs In phase: waves (or particles) are moving together, peaks line up with peaks and troughs line up with troughs Out of phase: waves (or particles) are not aligned; totally out of phase, peaks line up with troughs, troughs with peaks Out of phase: waves (or particles) are not aligned; totally out of phase, peaks line up with troughs, troughs with peaks Phase relationship can be expressed in degrees, related to circular motion Phase relationship can be expressed in degrees, related to circular motion

12 Frequency number of wave pulses passing a point in a given time number of wave pulses passing a point in a given time Measured from identical points on successive waves Measured from identical points on successive waves Symbol is f (or occasionally (nu)) Symbol is f (or occasionally (nu)) Unit is hertz (Hz), has SI units of sec -1 Unit is hertz (Hz), has SI units of sec -1 Old unit is cycles per second Old unit is cycles per second

13 Period Time for one wave cycle Time for one wave cycle Symbol is T Symbol is T Reciprocal of frequency T= 1/f Reciprocal of frequency T= 1/f

14 Wavelength Distance between identical points on successive waves Distance between identical points on successive waves Also distance wave travels in one period Also distance wave travels in one period Measured in meters (or parts of meters) Measured in meters (or parts of meters) Symbol is (lambda) Symbol is (lambda)

15 Wave Speed Same as any speed: distance/time, symbol v, units m/s Same as any speed: distance/time, symbol v, units m/s Depends on medium and often on  Depends on medium and often on  When speed depends on  in medium, medium is called dispersive When speed depends on  in medium, medium is called dispersive Causes dispersion, or spreading of wave according to wavelength; ex: rainbow Causes dispersion, or spreading of wave according to wavelength; ex: rainbow v =  / T = f v =  / T = f

16 Amplitude In transverse wave, equals maximum displacement from equilibrium position In transverse wave, equals maximum displacement from equilibrium position In longitudinal wave, equals maximum pressure change from normal pressure In longitudinal wave, equals maximum pressure change from normal pressure Damping by dissipative forces reduces amplitude as wave travels Damping by dissipative forces reduces amplitude as wave travels

17 Wave Properties Rectilinear Propagation Rectilinear Propagation Reflection Reflection Impedance Impedance Refraction Refraction Diffraction Diffraction Interference Interference

18 Rectilinear Propagation In uniform medium, waves travel in straight lines, perpendicular to wavefront In uniform medium, waves travel in straight lines, perpendicular to wavefront Wave velocity direction also perpendicular to wavefront Wave velocity direction also perpendicular to wavefront

19 Reflection Occurs at boundary between two media Occurs at boundary between two media Wave is returned to original medium Wave is returned to original medium Can be partial or complete depending on how new media transmits wave energy Can be partial or complete depending on how new media transmits wave energy The more wave speed changes at media boundary, the more wave is reflected The more wave speed changes at media boundary, the more wave is reflected Law of reflection: angle of incidence equals angle of reflection Law of reflection: angle of incidence equals angle of reflection

20 Law of Reflection

21 Impedance A measure of how easily a wave can be produced in a medium A measure of how easily a wave can be produced in a medium Equals ratio of applied force producing wave to resulting displacement velocity Equals ratio of applied force producing wave to resulting displacement velocity If impedances of two media match, wave is not reflected and is transmitted with no loss If impedances of two media match, wave is not reflected and is transmitted with no loss Impedance matching using transformers important for energy transmission systems Impedance matching using transformers important for energy transmission systems

22 Impedance and Reflection If wave can’t create displacement in particles of new media, impedance is infinite, wave is reflected out of phase: fixed end reflection If wave can’t create displacement in particles of new media, impedance is infinite, wave is reflected out of phase: fixed end reflection If wave producing force can’t be transferred to new media, impedance is zero and wave is reflected in phase: free end reflection If wave producing force can’t be transferred to new media, impedance is zero and wave is reflected in phase: free end reflection

23 Refraction Bending of wave path at boundary between media Bending of wave path at boundary between media Due to different wave speed in new medium Due to different wave speed in new medium Wave must strike boundary obliquely Wave must strike boundary obliquely Since v = f, change in speed changes Since v = f, change in speed changes If v in new media < v in old media, wave bends towards normal of boundary & vice versa If v in new media < v in old media, wave bends towards normal of boundary & vice versa

24 Refraction

25 Wave speed increases

26 Refraction Applet Refraction Applet

27 Diffraction Spreading of wave beyond edges of barrier or past small opening Spreading of wave beyond edges of barrier or past small opening Causes bending of wavefront Causes bending of wavefront Opening must be approximately same size as wavelength to diffract Opening must be approximately same size as wavelength to diffract Example: sound waves diffracted by doorways, light waves aren’t Example: sound waves diffracted by doorways, light waves aren’t

28 Diffraction

29 Superposition Principle When two or more waves travel through the same space (medium) at the same time... When two or more waves travel through the same space (medium) at the same time... Each wave proceeds independently as though no other waves were present Each wave proceeds independently as though no other waves were present The resultant displacement of any particle is the vector sum of displacements each wave would give it alone. The resultant displacement of any particle is the vector sum of displacements each wave would give it alone. Produces complex waveforms Produces complex waveforms

30 Interference Effects due to two or more superposed waves of similar frequency Effects due to two or more superposed waves of similar frequency If 2 waves of same type and frequency are in phase, displacements add, creating greater amplitude -- constructive interference If 2 waves of same type and frequency are in phase, displacements add, creating greater amplitude -- constructive interference Same waves out of phase, resultant displacement is now difference, decreasing amplitude --destructive interference Same waves out of phase, resultant displacement is now difference, decreasing amplitude --destructive interference

31 Interference Patterns Often destructive and constructive interference happens in different places at same time, creates interference pattern Often destructive and constructive interference happens in different places at same time, creates interference pattern Points of zero displacement, complete cancellation are called nodes Points of zero displacement, complete cancellation are called nodes Points of max displacement called antinodes Points of max displacement called antinodes Total wave energy doesn’t change, just rearranged Total wave energy doesn’t change, just rearranged

32 Standing Waves Standing wave: produced by interference of 2 periodic waves of same amplitude and wavelength traveling in opposite directions Standing wave: produced by interference of 2 periodic waves of same amplitude and wavelength traveling in opposite directions Usually wave reflected onto itself Usually wave reflected onto itself Nodes remain stationary, energy remains standing at antinodes Nodes remain stationary, energy remains standing at antinodes Basis for all string and wind instruments Basis for all string and wind instruments


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