Question

A particular station of All India Radio, New Delhi, broadcasts on a frequency of $1,368\, kHz$ (kilohertz). The wavelength of the electromagnetic radiation emitted by the transmitter is : [speed of light, $\left.c=3.0 \times 10^{8} ms ^{-1}\right]$

• A. 219.3 m
• B. 219.2 m
• C. 2192 m
• D. 21.92 cm

Answer 1

The Correct Option is A

The question requires us to find the wavelength of the electromagnetic radiation emitted by a transmitter broadcasting at a frequency of \(1,368\, \text{kHz}\). We are given the speed of light as \(c = 3.0 \times 10^{8} \, \text{m/s}\). We can use the relationship between wavelength, frequency, and the speed of light to find the solution: 

Formula: The speed of light (\(c\)) is related to frequency (\(\nu\)) and wavelength (\(\lambda\)) by the equation:

\(c = \lambda \nu\)

Step-by-Step Calculation:

1. First, convert the frequency from kilohertz to hertz: \(\nu = 1,368 \, \text{kHz} = 1,368 \times 10^{3} \, \text{Hz}\)
2. Substitute the known values into the formula: \(\lambda = \frac{c}{\nu} = \frac{3.0 \times 10^{8} \, \text{m/s}}{1,368 \times 10^{3} \, \text{Hz}}\)
3. Calculate the wavelength: \(\lambda = \frac{3.0 \times 10^{8}}{1,368 \times 10^{3}} \approx 219.3 \, \text{m}\)

Conclusion: Therefore, the wavelength of the electromagnetic radiation emitted by the transmitter is approximately 219.3 meters. This matches the given option \(219.3 \, \text{m}\), which is the correct answer.

Elimination of other options:

• 219.2 m: Very close to the correct answer, but the calculation gives us 219.3 m.
• 2192 m: Incorrect because of a misplaced decimal point.
• 21.92 cm: Incorrect as it's much shorter than the calculated wavelength.

Thus, the correct answer is 219.3 m.