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# Physics/Path Difference

Question
Two radio antennas are separated by 100 meters along the north-south line. Both broadcase identical 3
MHz waves. You start at the midpoint between the two speakers and walk 600 meters east and then
800 meters north.
a) What is the phase difference between the waves at this point?
b) Is the interference at this point maximum constructive, maximum destructive, or something in
between? Justify.
c) If you now begin to walk farther north, does the signal strength increase, decrease or stay the
same? Explain.

Thanks.

Hello Maurice,

We need the wavelength of these waves. The relation that makes sense to me based on analysis of the units is
v = lambda*f, so
lambda = v/f = 3*10^8 m/s / 3*10^6 cycles/s = 100 m

a) Use Pythagoras to find the distances between you and the 2 speakers (or are they antennas?). Subtract those distances and find what fraction of 100 m that is. Multiply that fraction by 2*pi radians or 360 degrees, however you like to give phase angles.

b) The interference is maximum constructive for any phase angle that is an integer multiple of 2*pi radians, maximum destructive for any odd integer multiple of pi radians. If the phase angle was something between zero and 2*pi, the interference was between the extremes.

c) Imagine you went 10 m farther north. Redo the steps of a. Does the phase angle get closer to the condition for maximum constructive or maximum destructive?

I hope this helps,
Steve

Physics

Volunteer

#### Steve Johnson

##### Expertise

I would be delighted to help with questions up through the first year of college Physics. Particularly Electricity, Electronics and Newtonian Mechanics (motion, acceleration etc.). I decline questions on relativity and Atomic Physics. I also could discuss the Space Shuttle and space flight in general.

##### Experience

I have a BS in Physics and an MS in Electrical Engineering. I am retired now. My professional career was in Electrical Engineering with considerable time spent working with accelerometers, gyroscopes and flight dynamics (Physics related topics) while working on the Space Shuttle. I gave formal classroom lessons to technical co-workers periodically over a several year period.

Education/Credentials
BS Physics, North Dakota State University
MS Electrical Engineering, North Dakota State University