Question

The intensity of sound from a point source is $1.0\times {10}^{-6}{m}^{-2}$ at a distance of 5.0 m from the source. What will be the intensity at a distance of 25 m from the source?

• A. $0.06\times {10}^{-8}W{m}^{-2}$
• B. $0.08\times {10}^{-8}W{m}^{-2}$
• C. $1\times {10}^{-8}W{m}^{-2}$
• D. $0.04\times {10}^{-8}W{m}^{-2}$

Answer 1

The correct option is D

$0.04\times {10}^{-8}W{m}^{-2}$

The power of the sound wave is intensity $\times$ surface area

power $=1\times {10}^8\times 4\pi \times 25$

$=100\pi {10}^{-8}={10}^{-6}\pi W$

Intensity at 25m $=\frac{power}{surfacearea}$

$=\frac{{10}^{-6}\pi }{4\pi (25{)}^2}$

$=\frac{{10}^{-6}}{625\times 4}$

$=\frac{{10}^{-6}}{2500}$

$=0.04\times {10}^{-8}W{m}^{-2}$