Question

Vijayawada FM radio station broadcasts at frequency of 103.4 MHz. The wavelength of the corresponding radio waves (in m) is

• A. 2.90
• B. 29.0
• C. 9.20
• D. 92.0

Hint:

To convert MHz to Hz, multiply by \(10^6\). The formula \( \lambda = \frac{c}{f} \) is crucial for calculating the wavelength of radio waves.

Answer 1

The Correct Option is A

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: \[ \lambda = \frac{3 \times 10^8 \, \text{m/s}}{103.4 \times 10^6 \, \text{Hz}} = 2.90 \, \text{m} \]

Answer 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.