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Calculating path difference
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lolz1411
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#1
Two coherent waves have a wavelenth of λ. The phase differen when they meet is 90 degrees (pi/2 radians). What could the path difference be :
(A) 2λ (B)λ (C) λ/2 (D) λ/4
I understand the formula for phase difference is:
Phase difference= 2 x pi x path difference/ λ
But seeing as none of the answers have pi in them, how am I meant to work this one out?
Thanks
(A) 2λ (B)λ (C) λ/2 (D) λ/4
I understand the formula for phase difference is:
Phase difference= 2 x pi x path difference/ λ
But seeing as none of the answers have pi in them, how am I meant to work this one out?
Thanks
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Drummy
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nevetstreblig
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#3
if they arrive 90 degrees out of phase, then (assuming we're talking a normal sin/cosine wave) then one wave is half a wavelength further down the time axis than the other
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Crowned Temmy
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phase difference = 90 degrees= pi/2
from your formula, path difference = ( phase difference * λ) / 2 pi
= (pi/2 * λ ) /2 pi
= λ/4
from your formula, path difference = ( phase difference * λ) / 2 pi
= (pi/2 * λ ) /2 pi
= λ/4
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spongpop
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i dont understand the difference between the path difference and ohase difference can anyone help please asap 
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goodfellow
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#6
(Original post by spongpop)
i dont understand the difference between the path difference and ohase difference can anyone help please asap
i dont understand the difference between the path difference and ohase difference can anyone help please asap
So these two waves have a path difference 'd'.
What is the phase difference?
Well lets look at the equation for a wave first.
The phase is the term in the brackets, phase = kx -
tSo look at the bottom wave in the picture, it is shifted to the right by an amount. It travels farther by the path d.
So the top wave will have the equation:
the bottom wave will have the equation:
Then from comparing the two, we can see the 'phase difference' is "kd".
(Phase top) - (Phase bottom) = kd
So if a cos graph (which is behind a sin graph by an amount
) had a phase difference of 
it would be a sin graph.
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goodfellow
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#7
This might also help, derivation of the wave equation:
Recap on graph transformations:
(1) y = Af(x) stretches the graph of y = f(x) vertically by an amount A (multiply y-coords by A. This constant is called the amplitude.
(2) y = f(x - B) shifts the graph of y = f(x) to the right by an amount B.
(3) y = f[G(x)] squashes the graph of y = f(x) by an amount 1/G (Multiply x-coords by 1/G).
So if you take a sin graph and squash it by a factor of 99, there will be 99x as many peaks/troughs in a certain time. So its frequency has increased. (frequeny = number of peaks that pass a given point in a time) G has the unit and is given the name 'angular frequency'.
It has the equation
So if you have a wave, it could have the equation![y_{x,t} = Asin[{\omega}(x)]](https://www.thestudentroom.co.uk/latexrender/pictures/9f/9f8cc174d187126d1c4b2338cf815dfe.png "y_{x,t} = Asin[{\omega}(x)]")
.
If it is moving to the right at a speed v, in a time 't', it will have moved a distance 'vt'
So the equation becomes![y_{x,t} = Asin[{\omega}(x - vt)]](https://www.thestudentroom.co.uk/latexrender/pictures/94/94036368ebdb4319bdd021b360efe8ce.png "y_{x,t} = Asin[{\omega}(x - vt)]")
.
which some re-arranging:
K is called the wave number.
so the equation of the travelling wave is now:
.
Recap on graph transformations:
(1) y = Af(x) stretches the graph of y = f(x) vertically by an amount A (multiply y-coords by A. This constant is called the amplitude.
(2) y = f(x - B) shifts the graph of y = f(x) to the right by an amount B.
(3) y = f[G(x)] squashes the graph of y = f(x) by an amount 1/G (Multiply x-coords by 1/G).
So if you take a sin graph and squash it by a factor of 99, there will be 99x as many peaks/troughs in a certain time. So its frequency has increased. (frequeny = number of peaks that pass a given point in a time) G has the unit
and is given the name 'angular frequency'. It has the equation
So if you have a wave, it could have the equation
.If it is moving to the right at a speed v, in a time 't', it will have moved a distance 'vt'
So the equation becomes
. which some re-arranging:
K is called the wave number.
so the equation of the travelling wave is now:
.
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Crowned Temmy
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#8
(Original post by spongpop)
i dont understand the difference between the path difference and ohase difference can anyone help please asap
i dont understand the difference between the path difference and ohase difference can anyone help please asap
Path difference is the fraction of wavelength by which one wave leads or lags behind another.
Phase difference is the angle (in radians) by which one wave leads or lags behind another.
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spongpop
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iMeme69
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