Chapter 17: Q29P (page 508)

A source emits sound waves isotropically. The intensity of the waves $2.50 m$ from the source is ${1.91×10}^{-4} {W/m}^{2}$ . Assuming that the energy of the waves is conserved, find the power of the source.

Short Answer

Expert verified

The power of the source is $1.50 \times 10^{- 2} W$ .

Step by step solution

Given data

Intensity of the wave is $I = 1.91 \times 10^{- 4} {W/m}^{2}$
Radius $r = 2.5 0m$

Determining the concept

Intensity of the source is given as the rate of energy (power) per unit area. Let, that source be centered at the sphere, having area $4π r^{2}$ . From this, calculate the power of the source. P is the power of the source, r is the radius of the sphere, and I is the intensity of the source.

The expression for the power is given by,

$P = I \times A$

Here is the intensity and A is the area.

Determining the power of the source

To calculate the power of the source,

$P = I \times A$

Substitute $1.91 \times 10^{- 4} {W/m}^{2}$ for l and $4 π r^{2}$ for A into the above equation,

$P = (1.91 \times 10^{- 4} {W/m}^{2}) \times (4 π r^{2})$

Substitute for into the above equation,

role="math" localid="1661538919438" $\begin{array}{l} P = (1.91 \times 10^{- 4}) \times (4 \times 3.14 \times {(2.5)}^{2}) \\ = 1.50 \times 10^{- 2} W \end{array}$

Hence, the power of the source is $1.50 \times 10^{- 2} W$ .

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A source emits sound waves isotropically. The intensity of the waves $2.50 m$ from the source is ${1.91×10}^{-4} {W/m}^{2}$ . Assuming that the energy of the waves is conserved, find the power of the source.

Short Answer

Step by step solution

Given data

Determining the concept

Determining the power of the source

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A source emits sound waves isotropically. The intensity of the waves2.50mfrom the source is1.91×10-4W/m2. Assuming that the energy of the waves is conserved, find the power of the source.

Short Answer

Step by step solution

Given data

Determining the concept

Determining the power of the source

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Space Physics

Classical Mechanics

Physical Quantities And Units

Turning Points in Physics

Electricity

Electricity and Magnetism

Study anywhere. Anytime. Across all devices.

A source emits sound waves isotropically. The intensity of the waves $2.50 m$ from the source is ${1.91×10}^{-4} {W/m}^{2}$ . Assuming that the energy of the waves is conserved, find the power of the source.