Question

going to an outdoor concert, and you'll be standing near a You are speaker that emits 50 W of acoustic power as a spherical wave. What minimum distance should you be from the speaker to keep the sound intensity level below 94 dB? Express your answer to two significant figures and include the appropriate units.

Answer 1

Intensity in W/m²

$I = I_{o}*10^{\frac{\beta }{10}}$

$I = 10^{-12}*10^{\frac{94}{10}}$

$I = 10^{-12}*10^{9.4}$

$I =2.512*10^{-3} W/m^{2}$

For a spherical wave, assuming you stand at a distance R

$\frac{P}{4\pi R^{2}} =2.512*10^{-3}$

$\frac{50}{4\pi R^{2}} =2.512*10^{-3}$

$R = 39.799 m$