I have a problem in which there are two radio broadcasting towers places a given distance apart (136 m). Each tower is broadcasting at the same frequency as the other one, but the frequency (or rather the wavelength is what I am concerned about) can be adjusted to alter the interference at a point (Q) that is another given distance (41 m) away from one of the towers, making it 177 m distance away from the other tower since it is arranged in a line.(adsbygoogle = window.adsbygoogle || []).push({});

I am looking for the longest wavelength that will cause destructive interference at point Q.

Also, I am looking for the longest wavelength for which there will be constructive interference at point Q.

I know constructive interference occurs when the waves are in sync with each other and thus add, creating a stronger (higher amplitude) wave.

Destructive interference occurs when the waves are 1/2 wavelength out of sync with eachother and the waves cancel each other out.

I have a formula to describe the electric field of the waves,

E_1 = A*cos(omega*t + phi)

E_2 = A*cos(omega*t)

where omega is the angular frequency, t is time, and phi is the phase of the wave you begin watching it at.

One can modify the formula using the relationship between omega*t to be,

E = A*cos((2*pi / lamba)x + phi)

where lamba is the wavelength and x is the distance traveled.

So now I am loooking for the [longest] wavelength that can be emmited from tower A, travel 177 m, and either be in sync, or 1/2 cycle out of sync from a wave of the save wavelngth emmited from tower B and only traveling 41 m.

I cant seem to grasp the concept of how to do this and where real numbers fall in.

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# Homework Help: Interference Patterns

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