Roger is in a ship offshore and listening to a baseball game...

Roger is in a ship offshore and listening to a baseball game on his radio. He notices that there is destructive interference when seaplanes from the nearby Coast Guard station are flying directly overhead at elevations of $780 \mathrm{~m}, 975 \mathrm{~m}$, and $1170 \mathrm{~m}$. The broadcast station is $102 \mathrm{~km}$ away. Assume there is a $180^{\circ}$ phase shift when the EM waves reflect from the seaplanes. What is the frequency of the broadcast?

Key Concepts

Destructive Interference

Destructive interference is a phenomenon where two coherent waves of the same frequency meet with a phase difference such that they cancel each other out. This typically occurs when the phase difference is an odd multiple of 180° (or ? radians), leading to a reduction or cancellation of the net amplitude at the point of interference.

Phase Shift Upon Reflection

When an electromagnetic wave reflects off a surface, especially when moving from a medium of lower optical density to a higher optical density, it may undergo a phase shift. Specifically, a reflection from a medium producing a higher phase shift, often 180° (? radians), is important because it alters the conditions needed for interference to be constructive or destructive.

Path Difference in Wave Interference

The concept of path difference deals with the difference in the distances traveled by two waves originating from the same source. When waves follow different paths to a reception point, the difference in these paths results in a phase difference which, depending on the wavelength, can produce conditions for constructive or destructive interference.

Frequency and Wavelength Relationship

This concept relates to the fundamental wave equation, which states that the speed of a wave is the product of its frequency and wavelength. For electromagnetic waves in a vacuum or air, the speed of light is approximately 3x10^8 m/s. This relationship is crucial since knowing one allows the calculation of the other, particularly when dealing with interference effects that depend on the wavelength.

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