A particular station of All India Radio, New Delhi, broadcasts on a frequency of $1,368 ext{ kHz}$ (kilohert

Question

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

Accepted Answer

The wavelength ($\lambda$), frequency ($
u$), and speed of light ($c$) are related by the equation:
$$c = 
u \lambda \Rightarrow \lambda = \frac{c}{
u}$$

1.  **Identify Given Values:**
    *   Frequency ($
u$) = $1368 	ext{ kHz} = 1368 	imes 10^3 	ext{ s}^{-1}$ (or Hz)
    *   Speed of light ($c$) = $3.0 	imes 10^8 	ext{ m s}^{-1}$

2.  **Calculate Wavelength ($\lambda$):**
    $$\lambda = \frac{3.0 	imes 10^8 	ext{ m s}^{-1}}{1368 	imes 10^3 	ext{ s}^{-1}}$$
    $$\lambda = \frac{3000 	imes 10^5}{13.68 	imes 10^5} 	ext{ m}$$ (Adjusting powers for easier division)
    $$\lambda = \frac{3.0 	imes 10^8}{1.368 	imes 10^6} 	ext{ m}$$
    $$\lambda = 219.298... 	ext{ m}$$

3.  **Rounding:**
    Rounding to one decimal place, $\lambda \approx 219.3 	ext{ m}$.

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