Types, characteristics, properties Waves Types, characteristics, properties

Wave: definition 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 Propagates through a medium or space Transfers energy, not matter water wave, sound, light, x-ray, earthquake

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

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

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

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

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

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

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

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

Phase 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 Phase relationship can be expressed in degrees, related to circular motion

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

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

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

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

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

Wave Properties Rectilinear Propagation Reflection Impedance Refraction Diffraction Interference

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

Reflection Occurs at boundary between two media Wave is returned to original medium 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 Law of reflection: angle of incidence equals angle of reflection

Law of Reflection

Impedance A measure of how easily a wave can be produced in a medium 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 Impedance matching using transformers important for energy transmission systems

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 producing force can’t be transferred to new media, impedance is zero and wave is reflected in phase: free end reflection

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

Refraction

Wave speed increases

Refraction Applet

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

Diffraction

Superposition Principle 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 The resultant displacement of any particle is the vector sum of displacements each wave would give it alone. Produces complex waveforms

Interference 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 Same waves out of phase, resultant displacement is now difference, decreasing amplitude --destructive interference

Interference Patterns 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 max displacement called antinodes Total wave energy doesn’t change, just rearranged

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