waves + quantum Flashcards
when do waves superpose?
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superposition happens when two or more waves pass through each other
what happens during superpositioning? (simple)
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⋅ superposition happens when two or more waves pass through each other
⋅ the displacements of the waves combine at the instance where the waves cross
⋅ then the waves continue on separately
what is the principle of superposition?
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the principle of superposition states that “when two or more waves cross, the resultant displacement [of the new wave] equals the vector sum of the individual displacements of the waves”
what are the two types of interference?
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interference can be constructive or destructive
what are examples of constructive interference?
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examples of constructive interference are:
⋅ superposing of crest + crest = makes bigger crest
⋅ trough + trough = bigger trough
what are examples of TOTAL destructive interference?
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examples of total destructive interference are:
⋅ crest + equal size trough = nothing
⋅ (and vice versa)
what is needed for total destructive interference?
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⋅ the displacements that will cancel out each other completely (crest + trough) must be equal-sized
⋅ if the displacements are not equal-sized, the destructive interference will not be total, instead it will result in a smaller wave
what are examples of destructive interference?
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examples of destructive interference:
⋅ crest + not equal size trough = smaller wave
⋅ (and vice versa)
what is needed for the interference of waves to be noticeable?
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for the interference of waves to be noticeable, the two amplitudes combining should be nearly equal
what can you use phasors for?
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you can use phasors to show superposition
how do the features of a phasor relate to the features of a wave?
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⋅ the frequency of the phasors are the same as the frequency of the wave
⋅ the length of a phasor is the same length as the amplitude of the wave
how do you superimpose waves using phasors?
what does it mean if [two points on a] wave[s] are in phase?
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two points on a wave are in phase if they are both at the same point in the wave cycle
how many radians (or degrees) are in 1 complete wave cycle, and what does this mean?
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⋅ 1 complete wave cycle = 2π radians (or 360 degrees)
⋅ so the angle the phasor will move through is 2π radians (or 360 degrees)
when are points on a wave in phase?
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⋅ points on a wave are in phase if the phase difference between them is 0 or a multiple of 2π radians (or 360 degrees) (eg, 0, 2π, 4π, 6π)
what directions will the phasors of points that are in phase point?
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phasors of points in phase will point in the same direction
when are points in antiphase?
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points are in antiphase if the phase difference between them is an odd-number multiple of π radians (or 180 degrees) (eg, π, 3π, 5π)
what directions will the phasors of points that are in antiphase point?
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the phasors of points in antiphase will point in opposite directions
what does it mean if two points on a wave are in antiphase?
two points on a wave are in antiphase if they are both at complete opposite points in the wave cycle
what is phase difference
can points on waves only be in phase or antiphase?
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⋅ NO
⋅ points don’t have to just be in phase or antiphase, they can have a phase difference of any angle
are waves usually in phase, and what does it mean if they are?
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⋅ in most situations, there will nearly always be a phase difference between two waves
⋅ if two waves ARE in phase, it’s usually bc the waves came from the same oscillator
what are the conditions to get clear interference patterns?
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to get a visible/clear interference pattern:
⋅ the two (or more) sources must be coherent
⋅ the displacements of the waves from the sources must be equal-sized
what happens to the interference pattern when the two (or more) sources are not coherent?
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⋅ if the two sources (or more) are not coherent, an interference will still happen, but it will not be clear