Question

Two sources as in phase and emit waves with λ=0.42m. Determine whether constructive or destructive interference occurs at points whose distances from the two sources are

(a) 0.84 and 0.42 m,
(b) 0.21 and 0.42 m,
(c) 1.26 and 0.42 m,
(d) 1.87 and 1.45 m,
(e) 0.63 and 0.84 m, and
(f) 1.47 and 1.26 m.

Answer 1

To determine whether constructive or destructive interference occurs at given points relative to two wave sources with a wavelength of 0.42m, the path difference must be considered. Constructive interference happens when this difference is a multiple of the wavelength, while destructive interference happens when it is half a wavelength longer.

Step-by-step explanation:

The question is concerned with the interference of waves, specifically whether constructive or destructive interference occurs at certain points given the distances from two wave sources. The phenomenon occurs when two in-phase waves with a wavelength (λ) of 0.42m meet.

The principle is that constructive interference occurs when the path difference between two waves is a multiple of the wave's wavelength, while destructive interference occurs when the path difference is half a wavelength longer than a multiple of the wavelength.

• (a) 0.84m and 0.42m have a path difference of 0.42m, which is λ, resulting in constructive interference.
• (b) 0.21m and 0.42m have a path difference of 0.21m, which is half of λ, resulting in destructive interference.
• (c) 1.26m and 0.42m have a path difference of 0.84m, which is 2λ, so it's constructive interference.
• (d) 1.87m and 1.45m have a path difference of 0.42m, which is λ, again resulting in constructive interference.
• (e) 0.63m and 0.84m have a path difference of 0.21m, which is half of λ, resulting in destructive interference.
• (f) 1.47m and 1.26m have a path difference of 0.21m, which is half of λ, so there is destructive interference.