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Chapter 20: Problem 2703

A radio can tune to any station in the 7. \(5 \mathrm{MHz}\) to $12 \mathrm{MHz}$ band. What is the corresponding wave length band? (A) \(400 \mathrm{~m}-250 \mathrm{~m}\) (B) \(40 \mathrm{~m}-25 \mathrm{~m}\) (C) \(4 \mathrm{~m}-2.5 \mathrm{~m}\) (D) None of these

Short Answer

Expert verified
The corresponding wavelength band for the given radio frequency range of 7.5 MHz to 12 MHz is 40 m - 25 m. Thus, the correct answer is option (B).

Step by step solution

01

Convert frequencies to hertz

To begin, we convert the given frequencies from MHz to Hz: \(7.5~MHz = 7.5 \times 10^6~Hz\) \(12~MHz = 12 \times 10^6~Hz\) The given frequency range is now 7.5 x 10^6 Hz to 12 x 10^6 Hz.
02

Find the lower limit of the wavelength band

Using the given formula, we find the longest wavelength corresponding to the lowest frequency: \(\lambda_1 = \frac{c}{f_1}\) \(\lambda_1 = \frac{3 \times 10^8~m/s}{7.5 \times 10^6~Hz}\) \(\lambda_1 = 40~m\) So, the lower limit of the wavelength band is 40 meters.
03

Find the upper limit of the wavelength band

Next, we find the shortest wavelength corresponding to the highest frequency: \(\lambda_2 = \frac{c}{f_2}\) \(\lambda_2 = \frac{3 \times 10^8~m/s}{12 \times 10^6~Hz}\) \(\lambda_2 = 25~m\) So, the upper limit of the wavelength band is 25 meters. The corresponding wavelength band for the given radio frequency is 40 m - 25 m, which corresponds to option (B).

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