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 electromagnetic radiation emitted by an All India Radio station in New Delhi, which broadcasts at a frequency of 1,368 kHz. To find the wavelength, we will use the formula that relates speed, frequency, and wavelength of a wave:

The formula is:

\(c = \lambda \cdot f\)

Where:

• \(c\) is the speed of light, \(3.0 \times 10^{8} \, \text{ms}^{-1}\)
• \(\lambda\) is the wavelength in meters
• \(f\) is the frequency in Hertz

Given:

• \(f = 1,368 \, \text{kHz} = 1,368 \times 10^{3} \, \text{Hz}\)

We rearrange the formula to solve for wavelength, \(\lambda\):

\(\lambda = \frac{c}{f}\)

Substituting the given values into the formula:

\(\lambda = \frac{3.0 \times 10^{8} \, \text{ms}^{-1}}{1,368 \times 10^{3} \, \text{Hz}}\)

Calculating the above expression:

\(\lambda = \frac{3.0 \times 10^{8}}{1.368 \times 10^{6}}\)

\(\lambda \approx 219.3 \, \text{m}\)

Thus, the wavelength of the electromagnetic radiation emitted by the transmitter is approximately 219.3 meters.

The correct answer is 219.3 m.

Explanation of the incorrect options:

• 219.2 m: Very close to the correct answer but slightly off due to rounding differences in final calculation.
• 2192 m: An order of magnitude greater than the actual calculated wavelength.
• 21.92 cm: Much smaller than the actual wavelength and incorrect conversion between units.