The frequency of transmission of a radio station is 30 MHz. Then the wavelengt of the waves transmitted by the centre will be `(v = 3 xx 10^(8) m//s)`

Options

A. 5m
B. 10m
C. 15 m
D. 20 m

Explanation

To find the wavelength of the waves transmitted by the radio station, we can use the formula that relates the speed of the wave (v), its frequency (f), and its wavelength (λ):

\[ v = f \cdot \lambda \]

Where:
- \( v \) is the speed of the wave,
- \( f \) is the frequency of the wave,
- \( \lambda \) is the wavelength of the wave.

### Step-by-step Solution:

1. **Identify the given values**:
- Frequency of the radio station, \( f = 30 \text{ MHz} \)
- Speed of the wave, \( v = 3 \times 10^8 \text{ m/s} \)

2. **Convert frequency from MHz to Hz**:
- \( 1 \text{ MHz} = 10^6 \text{ Hz} \)
- Therefore, \( 30 \text{ MHz} = 30 \times 10^6 \text{ Hz} = 3 \times 10^7 \text{ Hz} \)

3. **Rearrange the formula to solve for wavelength**:
\[ \lambda = \frac{v}{f} \]

4. **Substitute the values into the formula**:
\[ \lambda = \frac{3 \times 10^8 \text{ m/s}}{3 \times 10^7 \text{ Hz}} \]

5. **Simplify the expression**:
- The \( 3 \) in the numerator and denominator cancels out:
\[ \lambda = \frac{10^8 \text{ m/s}}{10^7 \text{ Hz}} = 10 \text{ m} \]

6. **Conclusion**:
- The wavelength of the waves transmitted by the radio station is \( \lambda = 10 \text{ m} \).