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 :
- 2.5
- 10
- 5
- 2
The Correct Option is C
Approach Solution - 1
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
Approach Solution -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 \( 5 \, \text{m} \).
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