If wavelength of an electromagnetic waves in free space is 0.075m, find its frequency.

Answer

To find the frequency of an electromagnetic wave given its wavelength in free space, we can use the relationship between wavelength (λ), frequency (ν), and the speed of light (c). The formula is given by:

\[ c = \lambda \cdot \nu \]

Where:
- \( c \) is the speed of light in vacuum, approximately \( 3 \times 10^8 \) meters per second.
- \( \lambda \) is the wavelength.
- \( \nu \) is the frequency.

### Step-by-step Solution:

1. **Identify the given values:**
- Wavelength (\( \lambda \)) = 0.075 m
- Speed of light (\( c \)) = \( 3 \times 10^8 \) m/s

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

3. **Substitute the known values into the equation:**
\[ \nu = \frac{3 \times 10^8 \text{ m/s}}{0.075 \text{ m}} \]

4. **Perform the division:**
- First, calculate \( 3 \times 10^8 \div 0.075 \):
\[ \nu = 3 \times 10^8 \div 0.075 = 4 \times 10^9 \text{ Hz} \]

5. **Conclusion:**
- The frequency of the electromagnetic wave is \( 4 \times 10^9 \) Hz.

### Final Answer:
The frequency of the electromagnetic wave is \( 4 \times 10^9 \) Hz.

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