Waves and Optics Chapters 16-17, 24-26 Physics Notes Waves and Optics Chapters 16-17, 24-26

Comparing Types of Waves Wave - the motion of a disturbance that transmits energy Comparing Types of Waves 1. Mechanical vs Electromagnetic Mechanical - requires a medium to transfer energy ie. slinky, water, sound, earthquake Electromagnetic - requires no medium ie. radio, micro, IR, visual, UV, X, gamma

3. Transverse vs Longitudinal Transverse – Particles or disturbance vibrate perpendicularly to the direction of energy transfer ie. light, slinky Longitudinal - Particles vibrate parallel to the direction of the energy transfer (Pressure Wave) compression vs rarefraction ie. sound, slinky http://www.phy.ntnu.edu.tw/~hwang/waveType/waveType.html http://www.explorescience.com/activities/Activity_page.cfm?ActivityID=50

Transverse Waves

Transverse and Longitudinal Waves

Aspects of all SHM (including waves) Amplitude (A) - maximum displacement from equilibrium (m) Intensity or Energy Period (T) - time to complete 1 cycle of motion (sec) Frequency (f) - number of cycles per unit time (Hz) T = 1 f = 1 f T

More Characteristics of Waves Crest and Trough- the highest and lowest points from the equilibrium position Wavelength (l) - The distance between two adjacent similar points of a periodic wave (m) Node - Position on a standing wave that has no displacement Antinode – Position on a standing wave that is displaced to its maximum displacement

Standing Wave – when two waves traveling in opposite directions interfere The waves must have the same f, A, and l Points of complete constructive and destructive interference http://www.phy.ntnu.edu.tw/~hwang/waveType/waveType.html

Standing Waves

In Phase – points on a wave in the same point in their cycle Which points are in phase? C and F How many degrees out of phase are these 2 waves? 90

V = [F/ (m/L)] ½ The Speed of a Wave on a string or spring Add Example Problem

V = d t V = f l = l T f = 1 The Speed of a Wave The speed of sound in air is 331 m/s The speed of light in a vacuum is 3.00 x 108 m/s = c Add Example Problem

*Notes from “Activity: Waves and Springs” What happens to a wave form when there is a disturbance in the medium through which it is traveling??? Standing Waves Wave interactions Interference: Constructive Destructive

Constructive Interference

Destructive Interference

Reflection of a Pulse

Sound Sound waves are __________ and ___________. Pitch - how high or low we perceive sound to be, depending on the frequency of the sound wave The audible range for humans is 20 Hz to 20,000 Hz. Ultrasonic waves: Medical applications, animal communication, others... Speed of sound depends on the medium in which it is traveling in. Speed generally increases with: denser phase higher temperature

Sound does not travel in a linear wave as we sometimes model it Sound does not travel in a linear wave as we sometimes model it. It really travels in 3D. Wave fronts - the concentric spheres of compression radiating from the source of the sound

V – Velocity of Sound (331 m/s) Doppler Effect - frequency shift that is the result of relative motion between the source of waves and an observer moving towards f1 = f / (1 - Vs/V) moving away f1 = f / (1 + Vs/V) f = emitted frequency f1 = perceived frequency V – Velocity of Sound (331 m/s) Vs – Relative velocity of the Source Hear the Doppler Effect Great Physlet http://webphysics.davidson.edu/applets/applets.html Click here to see the video of a plane breaking the sound barrier http://www.brewsterschools.org/brewster/brewsterhigh/plamoreaux/assets/sonicboom.mpg Know Red Shift and Blue Shift

Doppler Effect

Intensity - rate at which energy flows through a unit area perpendicular to the direction of wave motion intensity = P = P A 4pr2 Decibel Level (dB) - relative intensity of sound (logarithmic relationship)

Natural frequency - certain frequency at which an object vibrates Resonance - a condition that exists when the frequency of a force applied to a system matches the natural frequency of vibration of the system. Disastrous effects from earthquakes or winds http://www.regentsprep.org/Regents/physics/phys04/bresonan/default.htm

Harmonics fundamental frequency - the lowest frequency of vibration of a standing wave harmonic series - series of frequencies that includes the fundamental frequency and integral multiples of the fundamental frequency (overtones) Standing wave on a vibrating string Pipe open at both ends Pipe closed at one end

Beat - interference of waves of slightly different frequencies traveling in the same direction, perceived as a variation in loudness interference: constructive and destructive f beat = (f1 - f2 ) or (f2 - f1 ) Create and Hear Beats: http://explorescience.com/activities/Activity_page.cfm?ActivityID=44

Light waves are __________ and __________. Electromagnetic Waves – a transverse wave consisting of oscillating electric and magnetic fields at right angles to each other

Radio, Micro, IR, light, UV, X, Gamma Range of l and f

Light Visible Spectrum (l = 700 nm to 400 nm) 700 nm = 700 x 10-9 m = 7.00 x 10-7 m Again, a range of colors: ROY G BV

v = f l = d/t c = f l Wave speed For light, (c = speed of light = 3.00 x 108 m/s) c = f l All electromagnetic waves move at the speed of light and behave with the characteristics of light, but they can not be detected by the eye

3 x 108 m x 1 year x 365 days x 24 hours x 3600 s Light Year – the distance that light travels in a year d = V x t = 3 x 108 m/s x 1 year now convert 3 x 108 m x 1 year x 365 days x 24 hours x 3600 s s 1 year 1 day 1 hour d = 9.46 x 1015 m

Luminous –vs- Illuminated Luminous Flux (P) - the rate at which visible light is emitted from a source. Unit = lumen (lm) or Watt Illuminance (E) - the rate at which light falls on a surface Unit = lux (lx) = lm/m2 or Watt/m2 or candela E = P = P (sphere) A 4pr2 Luminous –vs- Illuminated Luminous Intesity (l) – the luminuous flux that falls on an area of 1 m2 Unit – candela or candle power

Light Amplification by Simulated Emission of Radiation LASER - a device that produces an intense, nearly parallel beam of coherent light Light Amplification by Simulated Emission of Radiation Applications: Diffraction - the spreading of a wave into a region behind an obstruction energy is dispersed may result in areas of constructive and destructive interference Spectral Emissions and Absorption

= d sin q Single Slit Diffraction Double Slit Diffraction Maxima – Constructive Interference d sin q = m l Minima – Destructive Interference d sin q = (m + ½) l m = order of the maxima (0, 1, 2, 3…) d = distance between slits Single Slit Diffraction = d sin q d = width of slit

angle of incidence = angle of reflection What happens when waves interact with matter? Reflection - the turning back of waves at the surface of a substance angle of incidence = angle of reflection qi = qr both angles are relative to the normal at the point of contact virtual image - an image formed by light rays that only appear to intersect flat mirror-

Mirrors Convex/Concave Virtual/Real Upright/Inverted Radius of Curvature and Focal Length Object and Image Distance Magnification

Mirrors 1 + 1 = 1 so si f Magnification M = h1 = - si h so

Mirror Notes and Equations * Given through “Activity: Concave and Convex Mirrors” Convex/Concave Virtual/Real Upright/Inverted Radius of Curvature and Focal Length Object and Image Distance Magnification Great Physlet http://www.phy.ntnu.edu.tw/java/Lens/lens_e.html

Reflection: The color that we perceive an object to be is the color of the light which that object reflects

Light Amplification by Simulated Emission of Radiation LASER - a device that produces an intense, nearly parallel beam of coherent light Light Amplification by Simulated Emission of Radiation Applications:

Polarization: The alignment of transverse waves in such a way that their vibrations are parallel to each other -some crystals naturally polarize -polymers -double polarization -applications: reflected glare is generally horizontal

Refraction: The bending of wave disturbance as it passes at an angle from one medium into another different media result in different speeds of transmission Index of Refraction (n): -ratio of speeds of light n = c v

n1 (sin q1) = n2(sin q2) n2 = V1 = l1 n1 V2 l2 The degree of refraction is determined by: Snell’s Law n1 (sin q1) = n2(sin q2) know bending towards or away As a wave travels from a medium to another velocity and wavelength change, but frequency does not. n2 = V1 = l1 n1 V2 l2

Dispersion – when white light separates into the spectrum of colors - results because different wavelengths travel at different speeds and refract differently

Total Internal Reflection - the complete reflection of light at the boundary of two transparent media; this effect occurs when the angle of incidence exceeds the critical angle Critical angle sin qc = nr ni only when ni > nr

converging lenses vs diverging lenses Lens - a transparent object that refracts light rays, causing them to converge or diverge to create an image converging lenses vs diverging lenses focal point (f) for a lens is the image distance for an object at an infinite distance f is: + for converging, - for diverging Ray Diagrams: 3 reference rays Is the Image: Real or Virtual Upright or Inverted Enlarged or Smaller

For lenses, the distance equation is similar to that of mirrors 1 + 1 = 1 so si f Magnification M = h1 = - si h so Lenses: the eye glasses - combination of lenses

Lens Power P =1 f Unit: diopter (D)