a) 2.5 m
The condition for constructive interference to occur is
[tex]|d_A-d_B|=m \lambda[/tex] (1)
where
dA is the distance of the point from source A
dB is the distance of the point from source B
m is an integer number
[tex]\lambda=6.0 m[/tex] is the wavelength of the wave
We immediately notice that solutions to the equation are only possible if m=0: otherwise, the difference between dA and dB would be at least 6.0 m, which is impossible since the two sources have a separation of 5.0 m (and we are considering only points between the two sources). Therefore we have
[tex]d_A - d_B = 0\\d_A = d_B = \frac{5.0 m}{2}=2.5 m[/tex]
So, constructive interference occurs halfway between the two sources.
b) 1 m, 4 m
The condition for destructive interference to occur is
[tex]|d_A-d_B|=(m+\frac{1}{2}) \lambda[/tex] (1)
As before, solutions are only possible for m=0, otherwise the point would not lie between the two sources.
So for m=0, we have:
[tex]|d_A - d_B| = \frac{\lambda}{2} = 3[/tex]
So, the two possible solutions are (using [tex]d_B = 5- d_A[/tex])
[tex]d_A = d_B + 3 \\d_A = (5-d_A)+3\\2d_A = 5+3 = 8\\d=4[/tex]
and
[tex]d_B - d_A = 3\\(5-d_A)-d_A=3\\5-2d_A = 3\\2d_A = 2\\d_A = 1[/tex]
So, the solutions are dA= 1 m and dA=4 m.
This is defined as the combination of two or more wave trains moving on intersecting or coincident paths.
Constructive interference = | da - db | = m λ wheredA is the distance of the point from source A, dB is the distance of the point from source B, m is an integer number, λ=6m.
da - db = 0
da=db= 5.0m/2 = 2.5m
Destructive interference
| da - db | = (m + 1/2) λ
| da - db | = λ/2
Two solutions with db = 5 - da
da = db + c
da = (5-da) + 3
2da = 8
da = 4.
db - da = 3
(5 - da) - da = 3
5 - 2da =3
2da = 2
da = 1
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