Three FM radio stations covering the same geographical area broadcast at frequencies 99.7, 99.9, and 100.1 MHz, respectively.

What is the maximum allowable wavelength width of the band-pass filter in a radio receiver such that the FM station 99.9 can be played free of interference from FM 99.7 or FM 100.1?

Use [tex]c = 3.0 \times 10^8 \text{ m/s}[/tex], and calculate the wavelength to an uncertainty of 1 mm. (State your answer to two significant digits.)

The maximum allowable wavelength width of the band-pass filter in a radio receiver to avoid interference from neighboring FM stations can be calculated using the formula wavelength = speed of light / frequency. The difference between the longest and shortest wavelengths gives the maximum allowable wavelength width of the band-pass filter.

Explanation:

The wavelength of a radio wave can be calculated using the formula:

Wavelength = Speed of Light / Frequency

Using the given information, we can calculate the wavelengths for the three FM radio stations:

FM 99.7: Wavelength = 3.0 x 108 m/s / 99.7 x 106 Hz = 3.0 m
FM 99.9: Wavelength = 3.0 x 108 m/s / 99.9 x 106 Hz = 3.003 m
FM 100.1: Wavelength = 3.0 x 108 m/s / 100.1 x 106 Hz = 2.997 m

To find the maximum allowable wavelength width of the band-pass filter, we need to calculate the difference between the shortest and longest wavelengths:

Maximum Wavelength Width = Longest Wavelength - Shortest Wavelength

Maximum Wavelength Width = 3.003 m - 2.997 m = 0.006 m

Therefore, the maximum allowable wavelength width of the band-pass filter is 0.006 m.

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