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Chapter 1: Q25E (page 1)

A jet plane at takeoff can produce sound of intensity \[10.0 {W \mathord{\left/

{\vphantom {W {{m^2}}}} \right.

\nulldelimiterspace} {{m^2}}}\]at \[30.0 m\]away. But you prefer the tranquil sound of normal conversation, which is\[1.0 {{\mu W} \mathord{\left/

{\vphantom {{\mu W} {{m^2}}}} \right.

\nulldelimiterspace} {{m^2}}}\]. Assume that the plane behaves like a point source of sound. (a) What is the closest distance you should live from the airport runway to preserve your peace of mind? (b) What intensity from the jet does your friend experience if she lives twice as far from the runway as you do? (c) What power of sound does the jet produce at takeoff?

Short Answer

Expert verified

(a) \(95\,km\)

Step by step solution

01

Given data

\(\begin{aligned}{l}{I_1} = 10.0\,{W \mathord{\left/

{\vphantom {W {{m^2}}}} \right.

\kern-\nulldelimiterspace} {{m^2}}}\\{I_2} = 1.0\,{{\mu W} \mathord{\left/

{\vphantom {{\mu W} {{m^2}}}} \right.

\kern-\nulldelimiterspace} {{m^2}}}\\{r_1} = 30.0\,m\end{aligned}\)

02

Concept/ Formula used

For a point source

\(I = \frac{P}{{4\pi {r^2}}}\)

\(\frac{{{I_1}}}{{{I_2}}} = \frac{{r_2^2}}{{r_1^2}}\)

03

Closest distance from Airport runaway

(a)

\(\begin{aligned}{c}\frac{{{I_1}}}{{{I_2}}} = \frac{{r_2^2}}{{r_1^2}}\\{r_2} = {r_1}\sqrt {\frac{{{I_1}}}{{{I_2}}}} \\ = 30\sqrt {\frac{{10\,{W \mathord{\left/

{\vphantom {W {{m^2}}}} \right.

\kern-\nulldelimiterspace} {{m^2}}}}}{{1 \times 1{0^{ - 6}}\,{W \mathord{\left/

{\vphantom {W {{m^2}}}} \right.

\kern-\nulldelimiterspace} {{m^2}}}}}} \\ = 95\,km\end{aligned}\)

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