To calculate the result of the superposition of two waves from coherent sources, we need to consider their phase difference and the principle of superposition for waves. The phase difference depends on the path length difference between the two sources.
Given that the wavelength of the microwaves is 10mm (0.01 meters), let's calculate the path length difference:
Path length difference (ΔL) = |Path length from Source 1 - Path length from Source 2|
Path length from Source 1 = 80 cm = 0.8 meters Path length from Source 2 = 75 cm = 0.75 meters
ΔL = |0.8 - 0.75| = 0.05 meters
Now, we need to find the phase difference (Δφ) between the two waves:
Phase difference (Δφ) = (2π/λ) * ΔL
where λ is the wavelength of the waves.
λ = 0.01 meters
Δφ = (2π/0.01) * 0.05 ≈ 10π radians
The result of the superposition of the two waves will depend on the value of Δφ. If Δφ is an integer multiple of 2π (i.e., 0, 2π, 4π, etc.), the waves will be in phase, and we will observe constructive interference. If Δφ is an odd multiple of π (i.e., π, 3π, 5π, etc.), the waves will be out of phase, and we will observe destructive interference.
Since Δφ ≈ 10π radians, it is neither an integer multiple of 2π nor an odd multiple of π. Therefore, the result of the superposition will be an intermediate case, resulting in a complex interference pattern where the amplitude and intensity of the resulting wave will vary at different points.
In summary, the superposition of two microwaves from coherent sources with wavelengths of 10mm, originating from points 80cm and 75cm apart, will result in an interference pattern with varying intensity across different regions. This pattern can be further analyzed using mathematical methods like Fourier analysis to understand the specific behavior of the superimposed waves.