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Chapter 2: Q27E (page 499)

Energy Output. By measurement you determine that sound waves are spreading out equally in all directions from a point source and that the intensity is \(0.026 {W \mathord{\left/

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

\kern-\nulldelimiterspace} {{m^2}}}\)at a distance of \(4.3 m\) from the source. (a) What is the intensity at a distance of \(3.1 m\) from the source? (b) How much sound energy does the source emit in one hour if its power output remains constant?

Short Answer

Expert verified

(a)\(0.050\,{W \mathord{\left/

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

Step by step solution

01

Given data

\(\begin{aligned}{l}{I_1} = 0.0261\,{W \mathord{\left/

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

{{m^2}}}\\{r_1} = 4.3\,m\\{r_2} = 3.1\,m\end{aligned}\)

02

Concept/ Formula used 

For point source,

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

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

03

Calculation for Intensity

(a)

\(\begin{aligned}{c}\frac{{{I_1}}}{{{I_2}}} = \frac{{r_2^2}}{{r_1^2}}\\{I_2} = {I_1}{\left( {\frac{{{r_1}}}{{{r_2}}}} \right)^2}\\ = \left( {0.0261\,{W \mathord{\left/

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

{{m^2}}}} \right){\left( {\frac{{4.3\,m}}{{3.1\,m}}} \right)^2}\\ = 0.050\,{W \mathord{\left/

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

{{m^2}}}\end{aligned}\)

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Most popular questions from this chapter

A simple harmonic oscillator at the point x = 0 gener ates a wave on a rope. The oscillator operates at a frequency of 40.0 Hz and with an amplitude of 3.00 cm. The rope has a linear mass density of 50.0 g/m and is stretched with a tension of 5.00 N. (a) Determine the speed of the wave. (b) Find the wavelength. (c) Write the wave function y(x, t) for the wave. Assume that the oscillator has its maximum upward displacement at time t = 0. (d) Find the maximum transverse acceleration of points on the rope. (e) In the discussion of transverse waves in this chapter, the force of gravity was ignored. Is that a reasonable approximation for this wave? Explain.

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