25 1 vibrations of a pendulum
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25.1 – vibrations of a pendulum. Period of oscillation only depends upon: Length of pendulum Acceleration of gravity Independent of mass Shorter = swings more often = higher frequency Example of simple harmonic motion (SHM). Masses on springs (honors). Masses on spring also exhibit SHM

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25 1 vibrations of a pendulum
25.1 – vibrations of a pendulum
  • Period of oscillation only depends upon:
    • Length of pendulum
    • Acceleration of gravity
  • Independent of mass
  • Shorter = swings more often = higher frequency
  • Example of simple harmonic motion (SHM)
masses on springs honors
Masses on springs (honors)
  • Masses on spring also exhibit SHM
  • Restoring force α distance from equilibrium
  • Bigger k = stiffer spring
  • Oscillating spring systems only depend upon:
    • Mass at end of spring
    • Spring constant
25 2 wave description
25.2 – wave description
  • Vibrations are what produces waves
    • Looks like a sine wave
  • # of cycles (vibrations) per second = frequency (f)
    • Unit: s-1 = hertz (Hz)
    • Period (T) = time for 1 cycle
25 3 wave motion
25.3 – wave motion
  • Waves transfer energy not matter
    • Only temporary motion of matter
    • No matter is transmitted between 2 points
    • The matter “bangs” into matter next to it, giving it energy
25 4 wave speed
25.4 – wave speed
  • Depends upon medium
  • Can be calculated as the distance a crests moves in a certain time
  • Fundamental relationship between: speed, wavelength & frequency
  • For the same type of wave – speed is the same
    • λ & f are inverses of one another
25 5 25 6 transverse longitudinal waves
25.5 & 25.6 – transverse & longitudinal waves
  • Wave pulse is perpendicular (across) from the direction of travel
    • EM waves need no medium to travel
  • Oscillation is back and forth in the direction of wave travel
    • Sound waves
electromagnetic waves
Electromagnetic waves
  • A self propagation of E & B fields
    • As one changes, so must the other
    • Moves at the speed of light, c = 3.00 x 108 m/s
    • Caused because of accelerating electric charges
slide8

Vibrations determine the frequency of EM waves

    • Visible light is just a sliver of EM spectrum
    • Includes: radio waves, microwaves, infrared, visible, ultraviolet, x-rays, gamma rays
    • In order of increasing energy
25 7 interference
25.7 - interference
  • When waves meet and overlap
  • Constructive interference
    • Waves meet & amplitude gets larger
  • Destructive interference
    • Amplitude gets smaller
  • When wave crests exactly line up – in phase
    • Not common
  • Out of phase when crest & trough overlap
    • Creates dark bands
25 8 standing waves
25.8 – standing waves
  • Waves generated have locations that appear to not move
  • Parts of wave that appear stationary – nodes
    • Complete destructive interference
    • Next to these are locations of maximum amplitude – antinodes – constructive int.
  • As waves meet, they interfere and then pass through one another
  • Higher frequency generate more standing waves
25 9 doppler effect
25.9 – doppler effect
  • The apparent change in frequency due to motion of source or observer
    • Waves move in all directions at same speed
    • Source moving “bunches up” waves in direction of motion & “spreads out” behind
slide12

Frequency is higher in direction of motion – a higher pitch

  • Occurs for all waves – sound & light
    • Blue shift – object towards us
    • Red shift - away
25 10 bow waves
25.10 – bow waves
  • Bow waves occur when wave source moves faster than the waves produced
25 11 shock waves
25.11 – shock waves
  • Shock waves are produced when object is faster than speed of sound
  • Caused because of constructive interference
  • Creates a conical shell of compressed air
  • This is the sonic boom
  • Always carried with plane (object) going ≥ vsound
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