Question

If frequency of electromagnetic wave is 60 MHz and it travels in air along z direction then the corresponding electric and magnetic field vectors will be mutually perpendicular to each other and the wavelength of the wave (in m) is :

• A. 2.5
• B. 10
• C. 5
• D. 2

Answer 1

The Correct Option is C

To determine the wavelength of an electromagnetic wave with a given frequency, we can use the fundamental relationship between the speed of light, frequency, and wavelength. The formula is given by:

\(c = \lambda \cdot f\)

Where:

• \(c\) is the speed of light in a vacuum, approximately \(3 \times 10^8 \, \text{m/s}\).
• \(\lambda\) is the wavelength of the electromagnetic wave.
• \(f\) is the frequency of the wave.

Given:

• Frequency, \(f = 60 \, \text{MHz} = 60 \times 10^6 \, \text{Hz}\).

We need to find the wavelength \(\lambda\) in meters.

Using the formula, we rearrange for \(\lambda\):

\(\lambda = \frac{c}{f}\)

Substitute the given values:

\(\lambda = \frac{3 \times 10^8}{60 \times 10^6}\)

Calculate \(\lambda\):

\(\lambda = \frac{3 \times 10^8}{60 \times 10^6} = \frac{3}{60} \times 10^2 = 0.05 \times 10^2 = 5\) meters.

Thus, the wavelength of the electromagnetic wave is 5 meters. Therefore, the correct answer is:

• 5

Answer 2

Given: - Frequency of the electromagnetic wave: \( f = 60 \, \text{MHz} = 60 \times 10^6 \, \text{Hz} \) - Speed of light in air: \( c = 3 \times 10^8 \, \text{m/s} \)

Step 1: Calculating the Wavelength

The wavelength \( \lambda \) of an electromagnetic wave is given by the formula:

\[ \lambda = \frac{c}{f} \]

Substituting the given values:

\[ \lambda = \frac{3 \times 10^8 \, \text{m/s}}{60 \times 10^6 \, \text{Hz}} \]

Simplifying:

\[ \lambda = \frac{3 \times 10^8}{60 \times 10^6} \, \text{m} \] \[ \lambda = \frac{3}{60} \times 10^2 \, \text{m} \] \[ \lambda = 5 \, \text{m} \]

Conclusion:

The wavelength of the electromagnetic wave is \( 5 \, \text{m} \).