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. Onthe 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 2.8 W ofsound power, and the radii of the concentric spheres are rA = 0.40 m and rB = 1.0 m.(a) Determine the sound intensity at each of the three patches. (b) The sound powerthat passes through each of the patches is 1.7 × 10-3 W. Find the area of each patch.

Answer 1

Dear student, please refer to the question:
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 2.3 W of sound power, and the radii of the concentric spheres are rA = 0.60 m and rB = 1.1 m.(a) Determine the sound intensity at each of the three patches. (b) The sound power that passes through each of the patches is 2.1 10-3 W. Find the area of each patch.

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 2.3 W of sound power, and the radii of the concentric spheres are rA = 0.60 m and rB = 1.1 m.(a) Determine the sound intensity at each of the three patches. (b) The sound power that passes through each of the patches is 2.1 �½ 10-3 W. Find the area of each patch.

Ans:

The relation between the power and intensity can be expressed as

$$ I=\frac{P}{A} $$

Since the area of surface is spherical area of sphere is \(A=4 \pi r^{2}\) Then above equation changes as

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

At \(r_{d}=0.60 \mathrm{~m}\) and \(2.3 \mathrm{~W}\) for \(P\)

$$ \begin{aligned} I_{1} &=\frac{2.3 \mathrm{~W}}{4 \pi(0.60 \mathrm{~m})^{2}} \\ &=0.51 \mathrm{~W} / \mathrm{m}^{2} \end{aligned} $$

The intensity of patch 1 and patch are same because they are at same distance

$$ I_{1}=I_{2}=0.51 \mathrm{~W} / \mathrm{m}^{2} $$

The intensity of out spherical surface is At \(r_{B}=1 . \mathrm{lm}\)

$$ \begin{aligned} I_{3} &=\frac{2.3 \mathrm{~W}}{4 \pi(1.1 \mathrm{~m})^{2}} \\ &=0.15 \mathrm{~W} / \mathrm{m}^{2} \end{aligned} $$

The area of patch 1 surface is

$$ \begin{aligned} A_{1} &=\frac{P}{I_{1}} \\ &=\frac{2.1 \times 10^{-3} \mathrm{~W}}{0.51 \mathrm{~W} / \mathrm{m}^{2}} \\ &=4.11 \times 10^{-3} \mathrm{~m}^{2} \end{aligned} $$

The area of patch 2 surface is

$$ A_{2}=\frac{P}{I_{2}} $$

$$ \begin{array}{l} =\frac{2.1 \times 10^{-3} \mathrm{~W}}{0.51 \mathrm{~W} / \mathrm{m}^{2}} \\ =4.11 \times 10^{-3} \mathrm{~m}^{2} \end{array} $$

The area of patch 3 surface is \(A_{3}=\frac{P}{I_{3}}\)

$$ \begin{array}{l} =\frac{2.1 \times 10^{-3} \mathrm{~W}}{0.15 \mathrm{~W} / \mathrm{m}^{2}} \\ =14 \times 10^{-3} \mathrm{~m}^{2} \end{array} $$

Answer 2

Dear student, please refer to the question:
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 2.3 W of sound power, and the radii of the concentric spheres are rA = 0.60 m and rB = 1.1 m.(a) Determine the sound intensity at each of the three patches. (b) The sound power that passes through each of the patches is 2.1 � 10-3 W. Find the area of each patch.

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 2.3 W of sound power, and the radii of the concentric spheres are rA = 0.60 m and rB = 1.1 m.(a) Determine the sound intensity at each of the three patches. (b) The sound power that passes through each of the patches is 2.1 �½ 10-3 W. Find the area of each patch.

Ans:

Answer 3

sorry