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Chapter 17: Q29P (page 508)

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

Expert verified

The power of the source is 1.50×10−2W.

Step by step solution

01

Given data

  • Intensity of the wave isI=1.91×10−4W/m2
  • Radiusr=2.50m
02

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 area4πr2. 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×A

Here is the intensity and A is the area.

03

Determining the power of the source 

To calculate the power of the source,

P=I×A

Substitute 1.91×10−4W/m2for l and4πr2 for A into the above equation,

P=(1.91×10−4W/m2)×(4πr2)

Substitute for into the above equation,

role="math" localid="1661538919438" P=(1.91×10−4)×(4×3.14×(2.5)2)=1.50×10−2W

Hence, the power of the source is 1.50×10−2W.

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