A radio can tune to any station in 7.5 MHz to 12MHz band. The corresponding wavelength band is

Options

A. 40 M to 25 m
B. 30 m to 25 m
C. 25 m to 10 m
D. 10 m to 5 m

Explanation

To find the corresponding wavelength band for a radio that can tune to frequencies between 7.5 MHz and 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: Convert frequencies from MHz to Hz
The frequencies given are:
- Minimum frequency \( f_1 = 7.5 \, \text{MHz} = 7.5 \times 10^6 \, \text{Hz} \)
- Maximum frequency \( f_2 = 12 \, \text{MHz} = 12 \times 10^6 \, \text{Hz} \)

### Step 2: Calculate the wavelength corresponding to the minimum frequency
Using the formula for wavelength:

\[ \lambda_1 = \frac{C}{f_1} \]

Substituting the values:

\[ \lambda_1 = \frac{3 \times 10^8 \, \text{m/s}}{7.5 \times 10^6 \, \text{Hz}} = 40 \, \text{m} \]

### Step 3: Calculate the wavelength corresponding to the maximum frequency
Using the same formula for wavelength:

\[ \lambda_2 = \frac{C}{f_2} \]

Substituting the values:

\[ \lambda_2 = \frac{3 \times 10^8 \, \text{m/s}}{12 \times 10^6 \, \text{Hz}} = 25 \, \text{m} \]

### Step 4: Determine the wavelength band
The corresponding wavelength band for the radio is from the minimum wavelength to the maximum wavelength:

\[ \text{Wavelength band} = 40 \, \text{m} \text{ to } 25 \, \text{m} \]

### Final Answer
The corresponding wavelength band is **40 m to 25 m**.

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