Question

A concert loudspeaker suspended high off the ground emits 31 W of sound power. A small microphone with a 1.0 cm^2 area is 42 m from the speaker. What is the sound intensity at the position of the microphone? (include units)
What is the sound intensity level at the position of the microphone? (in dB)

Answer 1

Answer:

intensity of sound at level of microphone is 0.00139 W / m 2

sound intensity level at position of micro phone is 91.456 dB

EXPLANATION:

Given data:

power of sound   P = 31 W

distance betwen microphone & speaker is   42 m

a) intensity of sound at microphone is calculated as

                   $I = \frac{P}{A}$

                   $= \frac{34}{4 \pi ( 44m )^ 2}$

                   =  0.00139 W / m 2        

b) sound intensity level at position of micro phone is

                $\beta = 10 log \frac{I}{I_o}$

    where I_o id reference sound intensity and taken as

                $= 1 * 10^{-12} W / m 2$  

               $\beta = 10 log\frac{0.00139}{10^[-12}}$

                     = 91.456 dB