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Wave formulas relating frequency and wavelength
- v = f λ
- velocity = (frequency)(wavelength)
- use only to find frequency or wavelength, velocity is independent of these two
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Frequency
the # of waves that pass a fixed point per second
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Period
- the # of seconds it takes for a complete wavelength to pass a fixed point
- T = 1 / f
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What factors affect the speed of a wave
- Only medium affects the velocity of a wave
- (1) its elasticity (resistance to change in shape) - stores U - greater eleasticity speeds waves up
- (2) its inertia (resistance to change in motion) - stores K.E. - greater inertia slows waves down
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Generally, stiff mediums ___ ___ waves.
speed, up
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Generally, heavy mediums ___ ___ waves.
slow, down
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What effect does temperature have waves traveling through a gas?
It increases velocity as it increases (more K.E.)
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Velocity relates to what for surface waves?
with surface waves, velocity increases with depth
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What is the elastic component of surface waves?
gravity
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How is power measured?
- Power is measured in terms of intensity (I)
- I is proportional to A2 and f2 for all waves
- It is related to itself - dB (decibles)
- ~ however many zeros you add to an intensity - take that integer and add a zero behind it, this will give you the decible jump
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Beats
- occurs when two waves with slightly different frequencies interfere with eachother
- at some points there are "in phase" (constructive) and sometimes they are out of phase (destructive)
- fbeat = | f1 - f2 |
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Pitch
- For sound waves, pitch correlates with frequency
- A high note will have a high pitch and a high frequency
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What happens to waves at an interface of media?
- (1) some (or all) of the energy is REFLECTED
- if it is reflected off of a more dense medium than the medium it is coming from --> the wave is inverted (180° phase shift)
- if it is reflected off a less dense medium --> the wave reflects back upright (no phase shift)
- (2) the remaining energy is REFRACTED into the new medium
- these waves will have the SAME frequency, a DIFFERENT wavelength, and a SMALLER amplitude
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Standing Waves
- waves that contain nodes and antinodes
- node is "still" when observed
- antinodes have the greatest displacement from zero
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Harmonic series
- a list of wavelengths that create standing waves for a specific length of "string"
- listed from largest to smallest
- ∴ 1st has the longest λ and the fewest nodes (2)
- if both ends are secure:
- L = nλn / 2 (n = 1, 2, 3...)
- if one end is loose:
- L = nλn / 4 (n = 1, 3, 5...)
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Simple Harmonic Motion
- motion that demonstrates a sine function of time
- objects in simple harmonic motion share certain properties: 1) acceleration is ∝ displacement but opposite in sign; 2) a & d are related by f2; 3) oscillates between kinetic and potential E
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The Doppler Effect
when a source moves relative to the observer it can change the frequency and the wavelength of the wave that reaches the observer
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Doppler Effect Formulas
- Δf / fs = v / c
- Δλ / λs = v / c
- fs: frequency produced by the source
- λs: wavelength produced by the source
- v: the net speed of the source and the object (if they are moving in the same direction you subtract their velocities; if they are moving in opposite directions you add their velocities)
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With the Doppler Effect, what happens as the source and the observer grow closer?
The frequency increases and the wavelength decreases
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What experiences no Doppler Effect?
- Objects moving in the same direction at the same speed
- v = 0 (because if they are moving in the same direction we subtract their speeds)
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