A radio can tune to any station to 7.3 MHz to 12 MHz band. The corresponding wavelength band is

Options

A. 25m-40m
B. 10m-30m
C. 20-40m
D. 25m-35m

Explanation

To find the corresponding wavelength band for the given frequency range of a radio that can tune from 7.3 MHz to 12 MHz, we can use the formula that relates wavelength (λ) to frequency (f):

\[ λ = \frac{c}{f} \]

where:
- \( λ \) is the wavelength,
- \( c \) is the speed of light (approximately \( 3 \times 10^8 \) m/s),
- \( f \) is the frequency in hertz (Hz).

### Step 1: Convert the frequencies from MHz to Hz
- The frequency range is given as 7.3 MHz to 12 MHz.
- Convert these frequencies to hertz:
- \( 7.3 \, \text{MHz} = 7.3 \times 10^6 \, \text{Hz} \)
- \( 12 \, \text{MHz} = 12 \times 10^6 \, \text{Hz} \)

### Step 2: Calculate the wavelength for the lower frequency (7.3 MHz)
- Using the formula:
\[ λ_{7.3} = \frac{c}{f_{7.3}} = \frac{3 \times 10^8 \, \text{m/s}}{7.3 \times 10^6 \, \text{Hz}} \]
- Calculate:
\[ λ_{7.3} = \frac{3 \times 10^8}{7.3 \times 10^6} \approx 41.1 \, \text{meters} \]

### Step 3: Calculate the wavelength for the upper frequency (12 MHz)
- Using the formula:
\[ λ_{12} = \frac{c}{f_{12}} = \frac{3 \times 10^8 \, \text{m/s}}{12 \times 10^6 \, \text{Hz}} \]
- Calculate:
\[ λ_{12} = \frac{3 \times 10^8}{12 \times 10^6} \approx 25 \, \text{meters} \]

### Step 4: Determine the wavelength band
- The corresponding wavelength band for the radio frequencies from 7.3 MHz to 12 MHz is from approximately 25 meters to 41.1 meters.

### Final Answer
The corresponding wavelength band is approximately **25 meters to 41.1 meters**.

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