Question

Let's compare the loudness of sound at different distances from two types of speakers: a home speaker operating at 1.00 Watts, and a concert venue speaker operating at 1000 Watts. Recall that normal room conversation is in the 60-80 dB range, while long-term damage to hearing can occur with chronic exposure in the 90-110 dB range. Sound greater than 120 dB exceeds the average threshold for pain, while even brief exposures to 140 dB sound can cause permanent hearing loss.

A small home speaker produces 0.200 W of acoustical power. (This is achieved, for example, by a 10-watt speaker operating at 2% electrical efficiency). If the speaker projects sound uniformly in all directions, what is the loudness of the sound (in dB) at a distance of 1.47 m from the speaker?

Answer 1

Answer:

98.67dB

Explanation:

To find the loudness of the sound you use the following formula:

$L_s(dB)=10log(\frac{I}{I_o})$     ( 1 )

I_o: threshold of hearing = 10^-12W/m^2

I: intensity of the sound = P/A=0.200W/(4pi r^2) (it is assumed that the sound wave is a spherical wave)

r: distance to the source of the sound

Then, by calculating I and replace it in (1) you obtain:

$I=\frac{P}{4\pi r^2}=\frac{0.200W}{4\pi(1.47m)^2}=7.365*10^{-3}W/m^2\\\\L_s(dB)=10log(\frac{7.365*10^{-3}W/m^2}{10^{-12}W/m^2})=98.67dB$

hence, the loudness of the sound is 98.67dB