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Physics 1080 Course Review

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University of Guelph
PHYS 1080
The Great Orbax

Travelling and Standing Waves  Biological phenomena are cyclic o Heartbeats o Circadian rhythms o Estrus Cycles What’s in a Wave?  Energy carrying disturbances  Produced by oscillations or vibrations  No overall forward movement of matter  Energy just moves  Waves have characteristic properties: o Wavelength, period, and speed  Waves can be deflected and interfere with each other CONSTRUCTIVELY or DESTRUCTIVELY Travelling wave: free to move through space Standing wave: -Reflected at both ends -Results in overlapping waves -Theory of superposition TRAVELLING WAVE  A disturbance which is free to move through space carrying ENERGY without the overall movement of MATTER Common types:  Matter waves: water, fluids, sound, electrical  EM waves: light, radio, UV, radar  Probability waves: quantum, electrons Properties of Travelling Waves:  Waves move energy NOT matter  Particles oscillate about an equilibrium point as wave “moves” TWO TYPES: Transverse: movement of oscillating particles is PERPENDICULAR to the direction of the wave propagation. Ex. Water, spring and light Longitudinal: movement of oscillating particles is PARALLEL to the direction of the wave propagation. Ex. Sound and slinky 1 SIMPLE HARMONIC MOTION  When forces act at 90 degrees of each other, they do not affect each other.  Pull the mass away from the spring, the spring exerts a force on the mass pulling it back towards equilibrium o Release mass o Fast pas equilibrium o Compress spring o Force back on mass by spring o Mass slows and stops, reverses direction of velocity o Shoots back past equilibrium o ETC. ****************This is called SHM**************** Oscillations and Travelling Waves:  Any movement of a particle which is displaced by a wave can be represented by a sinusoidal function y=A  Waves travel forward in both TIME & SPACE therefore we need a mathematical form of our wave which is dependent on both A= max displacement from equilibrium =angular frequency or change in angle wrt to time k= wave vector or change in angle wrt to time (+) or (-) according to direction of travel (+) negative direction (-) positive direction wt- TIME kx- POSITION 2 Wednesday September 12, 2011 SG1  Single particle on water’s surface  Oscillates back and forth in time exhibiting SHM  Time required to oscillate through one COMPLETE cycle is the PERIOD  Must go from MIN-MAX (must go through 2 - one complete cycle)  T=period=time for one cycle (sec) # of cycles or oscillations per unit time STANDING WAVES Friday September 15, 2011 Travelling- moves forward in time Standing- stationary (spatially trapped)  When it is reflected at a barrier, the returning wave is out of phase by radians (flips)  If there are barriers at both ends, there will be a reflection at bot ends and the waves will be constantly travelling back and forth *If the reflecting points are separated by a multiple of half a wavelength ( /2) then a STANDING WAVE is generated  Must be a half wave length Standing wave: a wave TRAPPED in one spatial location that has an oscillating AMPLITUDE Ex. Guitar string, organ pipes, auditory canal Two waves travelling in opposite directions in the same medium result in a standing wave du to principle of wave superposition. Ytotal y1+y2+y 3 (wave interference) Super position of waves Fourier’s Theorem 3 Constructive Interference:  Have 2 identical waves o Same frequency, amplitude and period  If in phase, create a standing wave o Keeps the same frequency and period but CHANGES amplitude Destructive Interference:  When a crest interferes with a trough and result in a small displacement o If crest and trough the same size, the displacement is 0 and it produces a complete cancellation  Two waves of the same wavelength travelling in opposite directions in the same medium result in a standing wave due to Theory of Superposition Incident wave (towards +x) Reflected wave (towards –x) 4 ACOUSTICS 1.4 1.5, 2.3 Monday September 19, 2011 Nature of Sound  Sound is a LONGITUDINAL wave  It is a wave of molecular displacements within regions of HIGH PRESSURE (compressions) and LOW PRESSURE (rarefaction)  Most displacement occurs in low pressure  Rarely a single frequency and a perfect sine wave  Same note from a string instrument (violin) or a vibrating air column (flute) have a different make up  There is a Fundamental Frequency (1 Harmonic) but also many higher harmonics which can overlap to create all the sounds we can hear Velocity of Sound  Longitudinal with frequency and wavelength  Moving through TIME and SPACE v= f  It is DEPENDENT on the medium it travels through  Sound travels FASTER in water than in air o Because easier to transmit vibrations in a DENSE medium  Frequency rang of human hearing is 20Hz20kHz  Women can hear better at higher frequencies than men o Evolutionary- crying baby Acoustic Resonance  When a sound wave or any wave is trapped within something like a tube or strong, a STANDING WAVE can be formed o Guitar string, flute, champagne glass 5 Beats  Consider the superposition of two waves of SLIGHTLY different frequencies but nearly equal intensities  Regions where the waves construct and destruct are what beats are  Perfect frequency perfect sine wave Beat cycle  time between minima in RESULTANT WAVE FB=|f2 2 | QUESTION:  Two tuning forks, one has a frequency of 350 Hz and 5 beats/sec is heard What is the frequency of fork 2? A: 355 Hz and 345 Hz ** because it’s an absolute value 6 ENERGY, POWER & INTENSITY  Sound is a disturbance in a medium  Energy is needed to create this disturbance o Units of energy: Joules  When you create a sound you use up energy which the wave then carries away in the form of vibrating molecules Power: defined as energy per time Intensity: defined as power per unit area - Governs loudness -Assume sound radiates equally in ALL directions -Assume sound energy is NOT absorbed (conservation of energy -Power of sound radiating out in circular waves -TOTAL energy (therefore total power) travelling through sphere 1 is equal to the TOTAL energy travelling through sphere 2 -TOTAL POWER and ENERGY is evenly distributed over the surface of this sphere  Sound is a travelling wave heading to your ear-it carries energy  The reason you can hear is because it vibrates the air molecules next to your ear v=wave speed (velocity- depending on what medium it’s in) f= frequency of wave A=amplitude of oscillation 7 INTENSITY & DECIBELS Loudness of Sound Pitch-frequency Loudness- intensity and intensity level Ear  Distinguishes SMALL differences in LOW intensity sounds and LARGE differences in HIGH intensity sounds  Survival  Perceived loudness therefore does NOT increase linearly with intensity- it increases logarithmically with INTENSITY Intensity level= perceived loudness OPTICS ch. 3  Light is considered to behave both as a particle and a wave Particle- light carries energy called QUANTA or PHOTON Energy of photon: E= hf Wave- light possesses many quantities of a wave Ex. Frequency, wavelength, speed  Light is a TRANSVERSE wave Visible Light  Visible light is part of the Electromagnetic (EM) Spectrum  400-700nm wavelength  White light is a mixture of ALL colours  All EM waves travel at speed of light in vacuum o c= 3.0 x 10 m/s  X-rays can destroy cells (ex. Cancer cells)  Visible light is also a TRANSVERSE wave Ray Model of Light  Light is treated as a travelling wave radiating uniformly from a source in all directions  Same wave emitted in 2 directions  The rays are always perpendicular to the wave fronts (therefore 90 ) and the direction of wave propagation  We treat light as a RAY when discussing its optical properties 8  Direction of the way called the direction of propagation is altered ONLY by reflection or refraction Refraction  When a ray of light is incident on a transparent interface, some of the light also ENTERS the second medium -Refracted light BENDSchanges direction  Light slows in denser media o Frequency does not change  In denser mediums the speed decreases but the time, period and frequency does NOT change  Wavelength gets smaller  Light travels within matter such as glass, plastic, water etc. Index of Refraction  Ratio of speed of light in vacuum to speed of light somewhere else  Since it is a ratio, it doesn’t have units *n is never less than one- n>1  N (index of refraction) measures how a medium slows light 9 Snell’s Law  Change in direction that occurs when a ray of light enters a medium Less densemore dense 2< 1 n 1n 2efraction gets CLOSER to normal More dense  less dense 2> 1 n 1n 2efraction gets FURTHER from normal Special Cases Straight thru 1= 0  2 = 0 10 Dispersion  Index of refraction is WAVELENGTH dependent  Light of different wavelengths bend differently THE EYE Crystalline lens- space between cornea, is filled with transparent fluid aqueous humor Ciliary muscle- attached to the lens and divides the eye into anterior and posterior chambers Posterior chamber is filled with vitreous humor Retina- layer of photoreceptor cells, nerve cells and nerve fibers Optic Nerve- region of no photoreceptors= blind spot Cornea- thin transparent film, which is kept in shape by the aqueous humor in the anterior chamber -Encloses the rest of the eye - Where most light bends Planar surfaces- cannot be used for focusing  The emergent beam is parallel to the incident beam if the same medium is on both sides of the glass  If the incident angle is zero, there is just a slight displacement which is usually too small to notice  You can never form an image with such a system even if you bend the glass o No deviation of the outgoing ray Refraction at Spherical Surface  Any ray perpendicular to the surface ( ) passes through the center of curvature o No refraction  Snell’s law bends light to normal  Curved surface refracts light so the rays pass through ONE POINT Power is additive POSITIVE power converges rays NEGATIVE power  diverges rays 11 Accommodation: the ability of the human eye to focus on both close objects AND distant objects Optical Defects of Eye NORMAL EYE:  Can relax and form the image of a DISTANT object on ret
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