For the same signal emitted by a radio antenna,

Observer A measures its intensity to be 16 times the

intensity measured by Observer B. The distance of

Observer A from the radio antenna is what fraction

of the distance of Observer B from the radio

antenna?

Answer: The distance of Observer A from the radio antenna is what fraction of the distance of Observer B from the radio antenna?

It is 1/4.

Step-by-step explanation:

We know that the intensity of electromagnetic waves decreases with the radius squared, this means that we can write a simple relation as:

Intensity (r) = A/r^2

Observer A measures 16 the intensity of observer B.

if Ia is the intensity that observer A measures and Ib is the intensity that observer B measures, we have that:

Ia = 16Ib

A / (ra) ^2 = 16*A / (rb) ^2

1 / (ra) ^2 = 16 / (rb) ^2

rb^2 = 16*ra^2

and we know that 16 = 4*4 = 4^2

rb^2 = (4*ra) ^2

then rb = 4*ra

this means that the distance between observer B and the antenna is equal to 4 times the distance between observer A and the antenna.

The fraction is ra = rb/4

The distance of

Observer A from the radio antenna is what fraction of the distance of Observer B from the radio antenna?

It is 1/4.