Explanation:
Given that,
Frequency of the AM radio station, [tex]f=1020\ kHz=1020\times 10^3\ Hz[/tex]
(a) Let [tex]\lambda[/tex] is the wavelength of this electromagnetic radiation. It can be calculated as :
[tex]\lambda=\dfrac{c}{f}[/tex]
[tex]\lambda=\dfrac{3\times 10^8\ m/s}{1020\times 10^3\ Hz}[/tex]
[tex]\lambda=294.11\ m[/tex]
Since the wavelength of one cycle is 294.12 m, then the total number of cycles over a 3 km distance is:
[tex]n=\dfrac{3000}{294.12}=10.19\ cycles[/tex]
Let the period is the duration of one cycle is given by:
[tex]T=\dfrac{1}{f}[/tex]
[tex]T=\dfrac{1}{1020\times 10^3}[/tex]
[tex]T=9.8\times 10^{-7}\ s[/tex]
So, total time required is t as :
[tex]t=n\times T[/tex]
[tex]t=10.19\times 9.8\times 10^{-7}[/tex]
[tex]t=9.98\times 10^{-6}\ s[/tex]
