Three FM radio stations covering the same geographical area...

Three FM radio stations covering the same geographical area broadcast at frequencies 91.1,91.3 , and $91.5 \mathrm{MHz}$, respectively. What is the maximum allowable wavelength width of the band-pass filter in a radio receiver such that the FM station 91.3 can be played free of interference from FM 91.1 or FM 91.5 ? Use $c=3.00 \cdot 10^{8} \mathrm{~m} / \mathrm{s}$, and calculate the wavelength to an uncertainty of $1 \mathrm{~mm}$

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Key Concepts

Frequency-Wavelength Relationship

This concept involves the fundamental relation c = ?f, where c is the speed of light, ? is the wavelength, and f is the frequency. It is essential for converting between the frequency domain and wavelength domain, which is particularly useful when designing filters or analyzing electromagnetic waves.

Band-Pass Filter Design

A band-pass filter allows signals within a specific frequency (or corresponding wavelength) range to pass through while rejecting signals outside that range. In the context of radio receivers, an appropriately designed band-pass filter ensures that only the intended station's signal is received, minimizing interference from neighboring frequencies.

Channel Spacing and Signal Interference

This concept addresses the importance of having sufficient spacing between broadcast channels to avoid interference. In FM radio systems, channels are separated by a certain frequency interval, and determining the maximum allowable filter width is critical to isolate the desired signal from adjacent ones, ensuring clear reception.

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