The velocity of all radio waves in free space is `3xx10^8 m//s`. The frequency of a radio wave of wavelength 150m is

Options

A. 20 kHz
B. 2 kHz
C. 2 MHz
D. 1 MHz

Explanation

To find the frequency of a radio wave with a given wavelength, we can use the formula that relates the speed of the wave (c), its frequency (ν), and its wavelength (λ):

\[ c = ν \times λ \]

Where:
- \( c \) is the speed of light in free space, approximately \( 3 \times 10^8 \) m/s.
- \( ν \) is the frequency in hertz (Hz).
- \( λ \) is the wavelength in meters (m).

### Step-by-step Solution:

1. **Identify the given values**:
- Speed of light, \( c = 3 \times 10^8 \) m/s
- Wavelength, \( λ = 150 \) m

2. **Rearrange the formula to solve for frequency (ν)**:
\[ ν = \frac{c}{λ} \]

3. **Substitute the known values into the equation**:
\[ ν = \frac{3 \times 10^8 \text{ m/s}}{150 \text{ m}} \]

4. **Perform the calculation**:
- First, divide \( 3 \times 10^8 \) by \( 150 \):
\[ ν = \frac{3 \times 10^8}{150} = 2 \times 10^6 \text{ Hz} \]

5. **Convert the frequency to megahertz (MHz)**:
- Since \( 1 \text{ MHz} = 10^6 \text{ Hz} \):
\[ ν = 2 \text{ MHz} \]

6. **Final answer**:
The frequency of the radio wave is \( 2 \text{ MHz} \).