Question

A concert loudspeaker suspended high off the ground emits 35 W of sound power. A small microphone with a 1.0 cm2 area is 50 m from the speaker. What are (a) the sound intensity and (b) the sound intensity level at the position of the microphone

Answer 1

Answer

given,

Power of sound   P = 35 W

Distance between micro phone and speaker = 50 m

small microphone Area = 1 cm²

a) intensity of sound at micro phone is

               $I = \dfrac{P}{A}$

               $I = \dfrac{35}{4\pi r^2}$

               $I = \dfrac{35}{4\pi\times 50^2}$

                      I = 1.11 mW/m²

b) sound intensity level at the position of micro phone is

 $\beta = 10 log (\dfrac{I}{I_0})$

      $\beta = 10 log (\dfrac{0.00111}{10^{-12}})$

      $\beta = 90.46 dB$