A source of sound is located at the center of two concentric spheres, parts of w

Question

A source of sound is located at the center of two concentric spheres, parts of which are shown in the drawing. The source emits sound uniformly in all directions. On the spheres are drawn three small patches that may or may not have equal areas. However, the same sound power passes through each patch. The source produces 2.2 W of sound power, and the radii of the concentric spheres are rA = 0.40 m and rB = 1.2 m.(a) Determine the sound intensity at each of the three patches. (b) The sound power that passes through each of the patches is 1.5 × 10-3 W. Find the area of each patch.

Explanation / Answer

power of the source P=2.2W

radius ra=0.4 m

radius rb=1.2 m

a)

at patch1

intensity I=P/4pi*r^2

I1=P/(4pi*ra)^2

I1=2.2/(4pi*0.4)^2

I1=8.71*10^-2 W/m^2

at patch2,

I2=P/(4pi*ra)^2

I2=2.2/(4pi*0.4)^2

I2=8.71*10^-2 W/m^2

at patch3

Intensity I=P/4pi*r^2

I3=P/(4pi*rb)^2

I3=2.2/(4pi*1.2)^2

I3=9.67*10^-3 W/m^2

b)

if power P=1.5*10^-3 W

I=P/area

forpatch1,

I1=P/A1

8.71*10^-2=1.5*10^-3/A1

====> A1=1.72*10^-2 m^2

forpatch2,

I2=P/A2

8.71*10^-2=1.5*10^-3/A2

====> A2=1.72*10^-2 m^2

forpatch3

I3=P/A3

9.67*10^-3=1.5*10^-3/A3

====> A3=0.155 m^2

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