Question

The Vividh Bharati station of All India Radio, Kozhikode, broadcasts on a frequency of \( 1500\,\text{kHz} \). What is the wavelength of the electromagnetic radiation emitted by the transmitter? \( (c = 3\times10^8\,\text{m s}^{-1}) \)

• A. \(200\,\text{m} \)
• B. \(300\,\text{m} \)
• C. \(100\,\text{m} \)
• D. \(250\,\text{m} \)
• E. \(150\,\text{m} \)

Hint:

Always convert kHz to Hz before using formula.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
All electromagnetic radiation, including radio waves, travels at the speed of light (\(c\)) in a vacuum. The relationship between the speed of light, frequency (\(f\)), and wavelength (\(\lambda\)) is fundamental to wave physics.
Step 2: Key Formula or Approach:
The formula connecting wavelength, frequency, and the speed of light is:
\[ c = f \times \lambda \] To find the wavelength (\(\lambda\)), we can rearrange the formula:
\[ \lambda = \frac{c}{f} \] Step 3: Detailed Calculation:
First, we must ensure all units are consistent. The speed of light is in m/s, so the frequency should be in Hertz (Hz), which is s\(^{-1}\).
Given frequency, \(f = 1500\) kHz.
We convert kilohertz (kHz) to hertz (Hz):
\[ 1 \text{ kHz} = 1000 \text{ Hz} = 10^3 \text{ Hz} \] \[ f = 1500 \times 10^3 \text{ Hz} = 1.5 \times 10^6 \text{ Hz} \text{ (or } s^{-1}) \] Given speed of light, \(c = 3 \times 10^8\) m/s.
Now, we can calculate the wavelength:
\[ \lambda = \frac{3 \times 10^8 \text{ m/s}}{1.5 \times 10^6 \text{ s}^{-1}} \] \[ \lambda = \left(\frac{3}{1.5}\right) \times 10^{(8-6)} \text{ m} \] \[ \lambda = 2 \times 10^2 \text{ m} = 200 \text{ m} \] Step 4: Final Answer:
The wavelength of the electromagnetic radiation is 200 m.