Question:
Vijayawada FM radio station broadcasts at frequency of 103.4 MHz. The wavelength of the corresponding radio waves (in m) is
Vijayawada FM radio station broadcasts at frequency of 103.4 MHz. The wavelength of the corresponding radio waves (in m) is
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To convert MHz to Hz, multiply by \(10^6\). The formula \( \lambda = \frac{c}{f} \) is crucial for calculating the wavelength of radio waves.
Updated On: Mar 18, 2026
- 2.90
- 29.0
- 9.20
- 92.0
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The Correct Option is A
Approach Solution - 1
We are given the frequency \( f = 103.4 \, \text{MHz} = 103.4 \times 10^6 \, \text{Hz} \). To calculate the wavelength, we use the formula:
\[
\lambda = \frac{c}{f}
\]
where \( c = 3 \times 10^8 \, \text{m/s} \) is the speed of light.
Substituting the values, we get:
\[
\lambda = \frac{3 \times 10^8 \, \text{m/s}}{103.4 \times 10^6 \, \text{Hz}} = 2.90 \, \text{m}
\]
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Approach Solution -2
Step 1: Use the wave equation to relate frequency and wavelength.
The speed of electromagnetic waves (including radio waves) is given by:
\[ c = \lambda \nu, \] where:
- \( c = 3.0 \times 10^8 \, \text{m/s} \) (speed of light),
- \( \lambda \) is the wavelength (in meters),
- \( \nu \) is the frequency (in Hz).
Step 2: Convert the given frequency into Hz.
\[ 103.4 \, \text{MHz} = 103.4 \times 10^6 \, \text{Hz} \]
Step 3: Rearrange the formula to solve for wavelength.
\[ \lambda = \frac{c}{\nu} = \frac{3.0 \times 10^8}{103.4 \times 10^6} \]
Step 4: Calculate the wavelength.
\[ \lambda = \frac{3.0 \times 10^8}{1.034 \times 10^8} = \frac{3.0}{1.034} \approx 2.90 \, \text{m} \]
Step 5: Conclusion.
The wavelength of the corresponding radio waves is 2.90 meters.
The speed of electromagnetic waves (including radio waves) is given by:
\[ c = \lambda \nu, \] where:
- \( c = 3.0 \times 10^8 \, \text{m/s} \) (speed of light),
- \( \lambda \) is the wavelength (in meters),
- \( \nu \) is the frequency (in Hz).
Step 2: Convert the given frequency into Hz.
\[ 103.4 \, \text{MHz} = 103.4 \times 10^6 \, \text{Hz} \]
Step 3: Rearrange the formula to solve for wavelength.
\[ \lambda = \frac{c}{\nu} = \frac{3.0 \times 10^8}{103.4 \times 10^6} \]
Step 4: Calculate the wavelength.
\[ \lambda = \frac{3.0 \times 10^8}{1.034 \times 10^8} = \frac{3.0}{1.034} \approx 2.90 \, \text{m} \]
Step 5: Conclusion.
The wavelength of the corresponding radio waves is 2.90 meters.
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