If velocity of radio waves is ` 3 xx 10^8 ` m/s, the frequency corresponding to wavelength of 300 m is

Options

A. 1 kHz
B. 10kHz
C. 1 MHz
D. 10 MHz

Answer

To find the frequency corresponding to a wavelength of 300 m for radio waves traveling at a velocity of \(3 \times 10^8\) m/s, we can use the formula that relates velocity (v), frequency (n), and wavelength (λ):

\[ v = n \cdot \lambda \]

### Step-by-Step Solution:

1. **Identify the given values**:
- Velocity of radio waves, \(v = 3 \times 10^8\) m/s
- Wavelength, \(\lambda = 300\) m

2. **Rearrange the formula to solve for frequency (n)**:
\[ n = \frac{v}{\lambda} \]

3. **Substitute the known values into the equation**:
\[ n = \frac{3 \times 10^8 \text{ m/s}}{300 \text{ m}} \]

4. **Simplify the calculation**:
- First, convert 300 m into scientific notation:
\[ 300 = 3 \times 10^2 \text{ m} \]
- Now substitute this back into the equation:
\[ n = \frac{3 \times 10^8}{3 \times 10^2} \]

5. **Cancel out the common terms**:
- The 3s cancel out:
\[ n = \frac{10^8}{10^2} \]
- Apply the laws of exponents:
\[ n = 10^{8-2} = 10^6 \text{ Hz} \]

6. **Convert Hz to MHz**:
- Since \(1 \text{ MHz} = 10^6 \text{ Hz}\), we have:
\[ n = 1 \text{ MHz} \]

### Final Answer:
The frequency corresponding to a wavelength of 300 m is \(1 \text{ MHz}\).

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