Answer :
Constructive interference between points A and B will occur at 2.5m from source A. Destructive interference between points A and B will occur 4m and 1m from source A.
Interference refers to a phenomenon where two waves are combined by adding their displacement together at every single point in space and time, to form a resultant wave of greater, lower, or the same amplitude. Constructive interference occurs when two waves overlap in a way to create a larger wave. Destructive interference occurs when two waves overlap in a way to cancel each other out.
The condition for constructive interference to occur is |dA-dB|=mλ
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, and λ is the wavelength = 6m.
Based on the condition, there can be one solution when m = 0 otherwise the difference between dA and dB would be at least 6m which is impossible as the sources are at a distance of 5m. Hence,
dA – dB = 0
dA = dB = 5/2 = 2.5m
The condition for constructive interference to occur is |dA-dB|=(m+1/2)λ
Based on the condition, the solution will occur when m = 0 otherwise the point will not be between source A and B.
Hence, when m = 0
|dA-dB|=(0+1/2)λ=λ/2=3
Using dB = 5 – dA to find the possible solutions.
dA = dB + 3
dA = 5 - dA + 3
2dA = 8
dA = 4m
and
dB – dA = 3
5 – dA – dA = 3
2dA = 2
dA = 1m
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