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, we can use the formula that relates wavelength (λ), frequency (ν), and the speed of light (c):

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

2. **Use the formula for frequency**:
The relationship between wavelength, frequency, and the speed of light is given by the equation:
\[ c = \lambda \cdot \nu \]
Rearranging this equation to solve for frequency (ν), we have:
\[ \nu = \frac{c}{\lambda} \]

3. **Substitute the known values**:
Now, substitute the values of c and λ into the equation:
\[ \nu = \frac{3 \times 10^8 \text{ m/s}}{0.075 \text{ m}} \]

4. **Calculate the frequency**:
To perform the division:
\[ \nu = \frac{3 \times 10^8}{0.075} \]
To simplify the calculation, we can convert 0.075 to a fraction:
\[ 0.075 = \frac{75}{1000} = \frac{3}{40} \]
Thus, we can rewrite the frequency calculation as:
\[ \nu = 3 \times 10^8 \div \left(\frac{3}{40}\right) = 3 \times 10^8 \times \frac{40}{3} \]
The 3s cancel out:
\[ \nu = 40 \times 10^8 = 4 \times 10^9 \text{ Hz} \]

5. **Final answer**:
Therefore, the frequency of the electromagnetic wave is:
\[ \nu = 4 \times 10^9 \text{ Hz} \]

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