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An Introduction to Interference
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An Introduction to Interference
What is Interference?
An Example and Application
You have a wave that has a wavelength of 5 m and it is in phase. What is the path difference? (assume n=1)
Solution: The waves are in phase so the waves are interfering constructively so we will use the formula:
Δx = (n)(lamda) = (1)(5 m) = 5 m.
- Two waves overlapping each other in the same medium
- Waves have same frequency and and wavelength, but vary in phase
- Interference can occur in one -dimensional or multi-dimensional waves - we will focus on two-dimensional waves for this presentation...
Path Difference
Khan Academy Video, Wave Interference
- The path difference is the difference in length that the two waves interfering travel
- (See image below) It is found by subtracting the distance of one point of the new wavelength of the combined waves (x2) from the other point of the wavelength (x1)
- The path difference allows us to determine whether constructive or destructive interference is occurring (see next slide).
Two Types of Interference
Constructive Interference
- Waves are in phase
- Amplitude of the waves add together
Destructive Interference
- Waves are out of phase
- Very small amplitude
Image - Yasmin Banga
Path Difference and Constructive Interference
Formula: Δx = n(lamda)
Δx = path difference
If n is a whole number (ie. 1,2, etc.), then path difference will be a whole number -- this scenario means the waves are interfering constructively.
*This is assuming that there is no wave source shift
Path Difference and Destructive Interference
Formula: Δx = (n+ 1/2) (lamda)
If the path difference equals a "half odd number" (ie. 1.5, 3.5, 5.5, etc.), then the waves are interfering destructively.
If the wave sources are shifted...
If one of the wave sources is shifter by π phase, then the formula for constructive interference becomes the formula for destructive interference, and vice-versa.
*This is assuming that there is wave source shift