Question

A particular AM radio station broadcasts at a frequency of 1020 kilohertz. What is the wavelength of this electromagnetic radiation?
1 m
How much time is required for the radiation to propagate from the broadcasting antenna to a radio 3 km away?
2 s

Answer 1

Explanation:

Given that,

Frequency of the AM radio station, $f=1020\ kHz=1020\times 10^3\ Hz$

(a) Let $\lambda$ is the wavelength of this electromagnetic radiation. It can be calculated as :

$\lambda=\dfrac{c}{f}$

$\lambda=\dfrac{3\times 10^8\ m/s}{1020\times 10^3\ Hz}$

$\lambda=294.11\ m$

Since the wavelength of one cycle is 294.12 m, then the total number of cycles over a 3 km distance is:

$n=\dfrac{3000}{294.12}=10.19\ cycles$

Let the period is the duration of one cycle is given by:

$T=\dfrac{1}{f}$

$T=\dfrac{1}{1020\times 10^3}$

$T=9.8\times 10^{-7}\ s$

So, total time required is t as :

$t=n\times T$

$t=10.19\times 9.8\times 10^{-7}$

$t=9.98\times 10^{-6}\ s$