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Interference, a question of path difference, or phase difference? Watch

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    Hello everybody!
    Im getting really confused when doing past papers about phase difference and path difference.
    I know that for constructive interference to occur the waves must have a phase difference of a multiple of 360, and a path difference of n lambda, with n being an integer.
    But is it possible to have a phase difference of 180 degrees and still constructively interfere? This may seem a bit vague I'm just not sure on how to word the question correctly.

    Thanks in advance!
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    I assume you mean two of the same wave (same \lambda)
    This picture shows the phase difference of 180, (\pi radians)
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    Here, the peaks align with the troughs and you get the resulting red line of 0 displacement. This is only true for a wave of \lambda = n(360) = n(2\pi) though, and so your rule only works for these types of waves. The example above has an example of \cos (x) and -\cos (x)
    For waves of path difference n \lambda the waves will always constructively interfere, where n is an integer and for waves where path difference k \lambda where k is a multiple of \frac{1}{2} the waves will always destructively interfere.

    The phase difference does not necessarily have to be 180 degrees though. If the wave has \lambda = 180 = \pi, the wave will actually constructively interfere at 180 phase difference, as there is a path difference of \lambda exactly. The picture below shows this:
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    Name:  WolframAlpha--sin_2x____sin_2x___sin_2x__sin_2x___Plots____2016_04_08_08_04.png
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    As stated, this shows waves with phase differences of 180 or \pi that constructively interfere to produce a bigger wave.
    So overall yes you can get two waves at a phase difference of 180 that constructively interfere, it is all dependant on the path difference not phase difference in this case.
    Hope this was helpful
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    Mmm

    I'd say it is always phase difference - but note that in the questions you'll get asked at A level it'll afaik either be single source with more than one path (typically because of reflection) or two sources that are emitting waves in phase, i.e. at 0 degrees phase difference (e.g. one signal generator connected to 2 loudspeakers)

    path difference is one cause of phase difference, because waves take time to cover distance, and it is the one you're likely to run into... but if for example you had 2 signal generators connected to 2 loudspeakers and they were emitting sound of the same frequency that wasn't in phase at the sources, the path difference to points of maxima and minima would be different than if the speakers were in emitting in phase.
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    (Original post by Joinedup)
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    Yes you're right, it is usually always phase difference and your examples work, I was just giving a more simple example where path difference was the main cause of interference, which in effect caused a phase difference :P
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    phase difference
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    Does anyone have any notes on path difference and phase difference?
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    I don't understand path difference and phase difference. Is there any relationship between the two?
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    Path difference is usually used when describing the extra distance traveled by a wave compared to the other if they are coherent. Like in the double slit experiment, where at the 1st order maxima one wave has traveled an extra distance of one wavelength compared to the other but as they are still in phase they interfere constructively producing a bright spot.
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    (Original post by JakeRStudent)
    Hello everybody!
    Im getting really confused when doing past papers about phase difference and path difference.
    I know that for constructive interference to occur the waves must have a phase difference of a multiple of 360, and a path difference of n lambda, with n being an integer.
    But is it possible to have a phase difference of 180 degrees and still constructively interfere? This may seem a bit vague I'm just not sure on how to word the question correctly.

    Thanks in advance!
    Phase difference of 180 degrees would mean the waves are in antiphase, so any interference would lead to only destrucive interference.
 
 
 
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