Always thinking ahead, Mr. H is investigating possible retirement communities in Flagstaff, Arizona. His favorite radio station in the Flagstaff area is KFIZ, broadcasting at 1420 kHz. One of the communities Mr. H is investigating is nestled in the cliffs, directly facing the KFIZ broadcasting station located several miles away. While driving through the neighborhood, Mr. H observes the KFIZ signal fading in and out. Mr. H reasons that the cause of the poor reception is that radio waves coming directly from the station undergoing are destructively interfering with waves which reflect off the cliffs from behind the retirement community. Knowing he must consider all factors in the purchase of a home, Mr. H decides to calculate all the possible distances from the cliffs for which destructive interference occurs. By doing so, he will be able to rule out the purchase of several lots in the neighborhood. Determine the six nearest distances from the cliffs that result in destructive interference of the 1420 kHz signal. (Assume that the reflected waves do not undergo a phase change upon reflection off the plane.)

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Read the problem carefully and develop a mental picture of the physical situation. If necessary, sketch a simple diagram of the physical situation to help you visualize it.

Identify the known and unknown quantities and record in an organized manner, often times they can be recorded on the diagram itself. Equate given values to the symbols used to represent the corresponding quantity (e.g., v = 3.00x10^{8} m/s, λ = 554 nm, f = ???).

Use physics formulas and conceptual reasoning to plot a strategy for solving for the unknown quantity.

Identify the appropriate formula(s) to use.

Perform substitutions and algebraic manipulations in order to solve for the unknown quantity.