The Inverse Square Law

Question

Hi, I have a hard time understanding the concept of the Inverse Square Law, and hence, answering this question. Please help!

 

The inverse square law for the intensity of light explains why we cannot pick up city radio stations in the country side. A radio station broadcasts at a frequency of 105.7 MHz. Their main office broadcasts at an intensity of 1.98x10⁴ Wbm^-2 (Assume intensity is at 1.0m distance).

a) How long would the radio signal take to travel to another city which is 32km away from their main office?

b) What is the wavelength of the radio station's waves?

 

Answer 1

You do not need to use the inverse square law to answer these 2 questions.  Just use basic wave relations.

 

(a)

 

c = speed of light = 3 x 10⁸ m/s

 

t = d/c = (32 x 10³ m) / (3 x 10⁸ m/s) ≅ 1.07 x 10^-4 s

 

(b)

 

λ = c/f = (3 x 10⁸ m/s) / (105.7 x 10⁶ Hz) ≅ 2.838 m