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25.1 – vibrations of a pendulum

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- 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 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- Frequency is higher in direction of motion – a higher pitch
- Occurs for all waves – sound & light
- Blue shift – object towards us
- Red shift - away

- Bow waves occur when wave source moves faster than the waves produced

- 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