Interference (15.5)
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Transcript of Interference (15.5)
WHAT IS INTERFERENCEWhen you combine 2 or more electromagnetic waves to form a resultant wave
Image fromPhysics for Scientists and EngineersAn interactive Approach
The image shows the crests 2 waves travelling in slightly different directions but with the same wavelength and frequencyIndicates moments when the waves are out of phase
Destructive interference
Indicates moments when the waves are in phaseInstructive inference
CONSTRUCTIVEConstructive interference occurs when the 2 waves (same frequency and wavelength) produced by 2 point sources are in phase
In terms of Path difference for constructive interference to occur:
Path difference between 2 sources must be an integer multiple of wavelength
In terms of radians or degrees,Path difference : integer of 360o or 2π
Wave 1
Wave 2
DESTRUCTIVEDestructive interference occurs when the 2 waves (same frequency and wavelength) produced by 2 point sources are out of phase
In terms of Path difference for destructive interference to occur:
Path difference for one of the source must be an integer multiple of wavelength and the other half an integer of wavelength
In terms of radians or degrees,Path difference : integer of 180o or π
Wave 2
Wave 1
PATH DIFFERENCEPath difference is the difference in length between two wavesCan be measured in wave length, radians and degrees
Constructive path difference Destructive path difference
In terms of :
Radians : 2πDegrees : 360o Wave length : λ
In terms of :
Radians : πDegrees : 180o Wave length : λ/2
Path difference equation : d2-d1 =√[ (x2- x1)2 + (y2-y1)2] – √[(x2- x1)2 – (y2-y1)2]______________ _____________
Where x1 and y1 are the coordinates of wave 1 and x2 and y2 are the coordinates of wave 2
TEST YOURSELFA person stands at a point where 2 waves with the same wave lengths and frequency interfere. What is the new path difference for the observer if he was located at x=4 and y=5. Could we say there is constructive or destructive interference?
(0,+1)
(0,-1)
TEST YOURSELF
1. Write out the path difference equation_____________ ____________
Hint: Use the equation for path difference
2. Plug in the x and y values, then solve
∆d =√[(4+0) 2 + (5-1)2] – √[4+0)2 – (5-1))2]∆d = √41 ∆d = 6.4
______________ _____________
As the value is neither an integer value of wave length, or an integer and a half value, there is neither destructive or constructive interference at the point where the observer stands
d2-d1 =√[ (x2- x1)2 + (y2-y1)2] – √[(x2- x1)2 – (y2-y1)(0,+1)
(0,-1)