Question

A certain source of sound waves radiates uniformly in all directions. At a distance of 14 m from the source the intensity level is 67 db. What is the total acoustic power output of the source, in watts? (Note: The reference intensity I 0 is 1.0 × 10-12 W/m2.)

Answer 1

Step-by-step explanation:

It is given that,

At a of 14 m from the source the intensity level is 67 db. We need to find the total acoustic power output of the source. The intensity level is given by :

`B=10\ dBlog((I)/(I_o))`

`I_o=10^(-12)\ W/m^2` (reference intensity)

`67\ dB=10\ dBlog((I)/(I_o))`

`6.7=\ dBlog((I)/(10^(-12)))`

`I=0.00000501\ W/m^2`

or

`I=5.01* 10^(-6)\ W/m^2`

Output power is given by :

`I=(P)/(A)`

`P=I* 4\pi r^2`

`P=5.01* 10^(-6)* 4\pi (14)^2`

P = 0.0123 watts

So, the output power of the source is 0.0123 watts. Hence, this is the required solution.