Answer :
Final answer:
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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