Waves

Waves

1. Waves

   • Wave Motion
     • Electromagnetic Waves
       • waves made of electric and magnetic fields that do not require medium 
     • Mechanical Waves
       • a wave that requires a medium through which to travel
   • Transverse & Longitudinal Waves
     • transverse: when particles of medium vibrate perpendicular to direction of motion of wave; has crests and troughs longitudinal: when particles of medium vibrate parallel to direction of motion of wave; has compressions and rarefactions
     • Basic Properties
       • Amplitude
         • the maximum displacement of particles of medium
       • Wavelength
         • the distance between similar points on consecutive waves
       • Frequency
         • # of waves per second
       • Speed
         • v = fλ
   • Resonance
     • natural frequency
       • frequencies at which system vibrates, which all objects have; depends on physical properties.
       • resonant frequency
         • the effect of the maximum vibration, when applied frequency = natural frequency.
     • forced vibration
       • vibration from external force
   • Interference
     • two waves traveling in same medium at same time experience interference
     • Constructive
       • when 2 waves combine so that amplitude of resulting wave is greater than either
     • Destructive
       • when 2 waves combine so that amplitude of resulting wave is less than either
     • Standing waves
       • produced when 2 waves of same frequency traveling in opposite directions in same medium interfere. 
       • Nodes
         • nodes are fixed points caused by destructive interference; because nodes remain in same positions, waves appear to be standing still.
       • Antinodes
         • the points directly between two nodes that experience max amount of displacement; result from constructive interference
       • Harmonics
         • natural frequencies
         • First Harmonic
           • the standing wave with 2 nodes and 1 antinode; longest λ and lowest frequency (fundamental frequency); all other harmonics are whole numbers of this.
   • Sound waves
     • longitudinal mechanical wave; any vibrating object produces sound
     • Frequencies
       • audible: 20-20,000Hz infrasonic: below 20Hz ultrasonic: above 20,000 Hz
     • Pitch
       • determined by frequency of sound wave; describes how high or low sound is; high f = high pitch
     • Music
       • consists of frequencies with obvious mathematical relationship: 2 waves with whole number ratio between frequencies interfere to form wave with repeating pattern
     • Beats
       • periodic, repeating fluctuations in intensity of sound that result when 2 waves with slightly different frequencies interfere; beat frequency = the difference in frequency of 2 notes that produce the beats
     • Doppler's Effect
       • produced by a relative change in frequency due to motion of sound of source or observer: as sound waves move forward from car, so does car. sound waves bunch up so frequency increases. f heard by observer is greater than source f, so pitch of sirens sounds higher.

2. Light

   • Electromagnetic Waves
     • produced by harmonic motion of charged particles at atomic level; consists of vibrating electric and magnetic fields at right angles to one another and to direction of motion of wave; transverse wave 
     • Electromagnetic Spectrum
   • Polarization
     • unpolarized light: vibrates in more than one plane polarized light: vibrates in one plane
     • Polarizing Filters
       • can be used to block out all but 1 direction of vibration so that remaining vibrations are only in one plane; two filters at 90 degree angles can block out all light.
   • Diffraction
     • process where light waves can bend around an obstacle or through an opening; amount of bending depends on relationship between λ and size of opening/obstacle:  if opening > λ, bending is unnoticeable if λ > opening; or sizes are closer to equal, bending is considerable
     • Single-Slit
       • as light passes through slit, they become semi-circular. screen placed a distance from slit shows large bright region in center + series of alternation light and dark spots on either side (interference fringes) that become smaller and fainter farther away from center.
     • Double Slit
       • as light passes through single slit, series of light and dark lines appear on screen, but two patterns overlap. the width of bright central region is proportional to λ
   • Speed of Light
     • 3 * 10^18 m/s

3. Optics

   • Reflection
     • process which light bounces off surface Law: angle of incidence is equal to angle of reflection; each angle is measured relative to the normal, perpendicular to surface
   • Mirrors
     • Plane
       • a flat mirror. light bounces off object and is reflected by the mirror. produces a virtual image; image is upright and same size as object; distance to the mirror is the same
     • Convex (diverging)
       • diverging mirror; curves towards object focal length is negative virtual, erect, smaller (VES)
     • Concave (converging)
       • converging; curves away from object focal length is positive Object is: > C: real, inverted, smaller (RIS) = C: real, inverted, equal (RIE) f>o>C: real, inverted, bigger (RIB) = f: none <f: virtual, erect, bigger (VEB)
     • Equations
       • 1/d(object) + 1/d(image) = 1/f M = hi/ho = -di/do
   • Refraction
     • bending of light: speed of light changes as it travels from one medium to another.  when ray enters straight into medium, entire ray speeds up or slows down together. at an angle, one part of ray changes speed before another, causing a bend. 
     • Index of Refraction
       • n = c/v(medium) the amount of bending: compares c in vacuum with c in medium.
     • Snell's Law of Refraction
       • n1sinΘ1 = n2sinΘ n1, n2 = indices of refraction for two mediums Θ1, Θ2 = angles of incidence and refraction
   • Total Internal Reflection
     • the process when light incident on boundary of two medium, (passing from medium with higher index of refraction; denser), is reflected back into original medium. Θ(incidence) = 0, light passes directly across
     • Critical Angle
       • the angle of incidence when angle of refraction is 90 degrees.  Θ(incidence) > Θ(critical), light is no longer refracted, only reflected back into medium
   • Lens
     • Convex (converging)
       • >2F: real, inverted, smaller (RIS) =2F: real, inverted, equal (RIE) F<o<2F: real, inverted, larger (RIL) =F: no image. <F: virtual, erect, larger (VEL)
     • Concave (diverging)
       • virtual, erect, smaller (VES)

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