two coherent sources of radio waves, a and b, are 5.00 meters apart. each source emits waves with wavelength 6.00 meters. consider points along the line connecting the two sources. 1) At what distance from source A is there constructive interference between points A and B?
2) At what distances from source A is there destructive interference between points A and B? Note that there will be two separate interference fringes between point A and point B.

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08-12-2022
Physics

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two coherent sources of radio waves, a and b, are 5.00 meters apart. each source emits waves with wavelength 6.00 meters. consider points along the line connecting the two sources. 1) At what distance from source A is there constructive interference between points A and B?
2) At what distances from source A is there destructive interference between points A and B? Note that there will be two separate interference fringes between point A and point B.

Answer :

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febyyyvaalentina febyyyvaalentina · Answer 1 · 2022-12-18T21:59:26-05:00

The distance from source A at which there is constructive interference between points A and B is 3.50 meters.
There will be two separate interference fringes between points A and B, with the first fringe occurring at 3.00 meters and the second fringe occurring at 6.00 meters.

The distance from source A at which there is constructive interference between points A and B can be found by setting the phase difference between the waves from sources A and B to a multiple of 2π. The phase difference between the waves at a given point is given by:

To determine the distance from source A at which there is constructive interference between points A and B, we can use the formula for the constructive interference of two waves:

d = (m + 1/2) *λ / 2

where d is the distance from source A, m is an integer, lambda is the wavelength of the radio waves, and the term (m + 1/2) is the phase difference between the two waves.

Plugging in the values given in the problem, we get:

d = (m + 1/2) * 6.00 meters / 2

= (m + 0.5) * 3.00 meters

Since we want constructive interference, the phase difference must be an integer multiple of 2π, which means the value of m must be an even integer. Therefore, we can set m = 2 to get:

d = (2 + 0.5) * 3.00 meters

= 3.50 meters

So the distance from source A at which there is constructive interference between points A and B is 3.50 meters.

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