A radio can tune to any station in 7.5 MHz to 12MHz 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 a radio that can tune to any station in the frequency range of 7.5 MHz to 12 MHz, we will use the formula that relates the speed of light (C), frequency (ν), and wavelength (λ):

\[ \lambda = \frac{C}{\nu} \]

Where:
- \( \lambda \) is the wavelength,
- \( C \) is the speed of light, approximately \( 3 \times 10^8 \) m/s,
- \( \nu \) is the frequency in Hz.

### Step 1: Calculate the wavelength for the lower frequency (7.5 MHz)

1. Convert the frequency from MHz to Hz:
\[ 7.5 \text{ MHz} = 7.5 \times 10^6 \text{ Hz} \]

2. Use the wavelength formula:
\[ \lambda_1 = \frac{C}{\nu_1} = \frac{3 \times 10^8 \text{ m/s}}{7.5 \times 10^6 \text{ Hz}} \]

3. Calculate \( \lambda_1 \):
\[ \lambda_1 = \frac{3 \times 10^8}{7.5 \times 10^6} = 40 \text{ meters} \]

### Step 2: Calculate the wavelength for the upper frequency (12 MHz)

1. Convert the frequency from MHz to Hz:
\[ 12 \text{ MHz} = 12 \times 10^6 \text{ Hz} \]

2. Use the wavelength formula:
\[ \lambda_2 = \frac{C}{\nu_2} = \frac{3 \times 10^8 \text{ m/s}}{12 \times 10^6 \text{ Hz}} \]

3. Calculate \( \lambda_2 \):
\[ \lambda_2 = \frac{3 \times 10^8}{12 \times 10^6} = 25 \text{ meters} \]

### Final Result

The corresponding wavelength band for the radio tuning range of 7.5 MHz to 12 MHz is between 25 meters and 40 meters.

### Answer
The corresponding wavelength band is from 25 meters to 40 meters.

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