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# 25.1 – vibrations of a pendulum PowerPoint PPT Presentation

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

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

• 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

• 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

• 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

• 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

• 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

• 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

### 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

• 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

• 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

### 25.10 – bow waves

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

### 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