Final answer:
Approximately 62 radio stations can operate in the given broadcast band range, from a 200-m to a 530-m wavelength, with each station requiring a specific frequency bandwidth of 15.0 kHz.
Step-by-step explanation:
Calculating the number of radio stations that can operate in a given broadcast band involves understanding the relationship between wavelength, frequency, and the bandwidth each station requires. First, the wavelength (λ) and frequency (f) of a wave are related by the speed of light (c): λ = c / f. For the radio broadcast band, we need to convert the given wavelength range to frequency, knowing that the speed of light is approximately 3.00×108 m/s.
The frequency for a 200-m wavelength is f = c / λ = 3.00×108 m/s / 200 m = 1.5×106 Hz or 1500 kHz. Similarly, the frequency for a 530-m wavelength is approximately 566 kHz. Hence, the frequency range for the broadcast band is 566 to 1500 kHz.
Now, since each station requires a 15.0 kHz band, the number of stations N is given by the range divided by the bandwidth per station. N = (1500 kHz - 566 kHz) / 15.0 kHz. Thus, approximately 62 stations can operate exclusively in this range.