Chapter 33: Q8P (page 1001)

Assume (unrealistically) that a TV station acts as a point source broadcasting isotopically at $1.0 MW$ . What is the intensity of the transmitted signal reaching Proxima Centauri, the star nearest our solar system, $4.3 ly$ away? (An alien civilization at that distance might be able to watchXFiles.) A light-year ( $l y$ ) is the distance light travels in one year.

Expert verified

The intensity of the transmitted signal reaching Proxima Centauri, the star nearest our solar system $4.3 ly$ is, $4.8 \times 10^{- 29} W / m^{2}$ .

Step by step solution

Source power

$\begin{array}{rcl} P_{s} & = & 1.0 MW \\ = & 1.0 \times 10^{6} W \end{array}$

Distance of the star is, $r = 4.3 ly$

The source is emitting power isotopically. The received power intensity depends on the source power and the distance.

Formula:

$I = \frac{P_{s}}{4 π R^{2}}$

The distance is given in light years, by converting it in to meters:

$1 ly = 9.46 \times 10^{15} m$

$\begin{array}{rcl} 4.3 ly & = & 4.3 \times 9.46 \times 10^{15} m \\ = & 4.068 \times 10^{16} m \end{array}$

Using the intensity formula:

$I = \frac{P_{s}}{4 π R^{2}}$

Substitute all the value in the above equation.

$\begin{array}{rcl} I & = & \frac{1.0 \times 10^{6} W}{4 π \times {(4.068 \times 10^{16} m)}^{2}} \\ = & 4.8 \times 10^{- 29} W / m^{2} \end{array}$

The intensity of the transmitted signal reaching Proxima Centauri, the star nearest our solar system, 4.3lyaway $4.8 \times 10^{- 29} W / m^{2}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.