Loading web-font TeX/Main/Regular

Wednesday, January 27, 2016

Sound intensity

Question:
There is a speaker emitting sound with a uniform power of 250 W. At what distance will the intensity be just below the threshold of pain, which is 1.00 W/m^2?

Answer:
The sound intensity is given by
I = \frac{P}{A}

The sound emitted uniformly in space, so it is spherically propagated. The area of sphere is 4\pi r^2. Thus,
I=\frac{P}{4\pi r^2}

Solve for the distance.
r^2 = \frac{P}{4\pi I} \\     r = \sqrt{\frac{P}{4\pi I}}

Plug in the numbers.
r = \sqrt{\frac{250 (\mathrm{W})}{4\pi \times 1.00 (\mathrm{W/m}^2)}}

Therefore, the distance is
r = 4.46 \mathrm{m}


Powered by Hirophysics.com

No comments:

Post a Comment