A radio can tune into any station in the `7.5 MHz` to `12 MHz` band. What is the corresponding wavelength of band?

Explanation

To find the corresponding wavelength of the band for a radio that can tune into frequencies from 7.5 MHz to 12 MHz, we can use the formula that relates the speed of light (c), frequency (f), and wavelength (λ):

\[ \lambda = \frac{c}{f} \]

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

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

1. Convert the frequency from megahertz (MHz) to hertz (Hz):
\[ f_1 = 7.5 \text{ MHz} = 7.5 \times 10^6 \text{ Hz} \]

2. Use the wavelength formula:
\[ \lambda_1 = \frac{c}{f_1} = \frac{3 \times 10^8 \text{ m/s}}{7.5 \times 10^6 \text{ Hz}} \]

3. Perform the calculation:
\[ \lambda_1 = \frac{3 \times 10^8}{7.5 \times 10^6} = 40 \text{ m} \]

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

1. Convert the frequency from megahertz (MHz) to hertz (Hz):
\[ f_2 = 12 \text{ MHz} = 12 \times 10^6 \text{ Hz} \]

2. Use the wavelength formula:
\[ \lambda_2 = \frac{c}{f_2} = \frac{3 \times 10^8 \text{ m/s}}{12 \times 10^6 \text{ Hz}} \]

3. Perform the calculation:
\[ \lambda_2 = \frac{3 \times 10^8}{12 \times 10^6} = 25 \text{ m} \]

### Step 3: Determine the wavelength range

The corresponding wavelength range for the radio band is from \( \lambda_1 \) to \( \lambda_2 \):
- Minimum wavelength \( \lambda_1 = 40 \text{ m} \)
- Maximum wavelength \( \lambda_2 = 25 \text{ m} \)

Thus, the corresponding wavelength of the band is from 25 meters to 40 meters.

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

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