Question

What is the speaker’s power output if the sound intensity level is 102 dBdB at a distance of 25 mm ? Express your answer to two significant figures and include the appropriate units.

Answer 1

Power = 124.50 W

Step-by-step explanation:

Given that:

The Sound intensity of a speaker output is 102 dB

and the distance r = 25 m

For the intensity of sound,

`\beta (dB)= 10 \ log_(10 ) ((I)/(I_o))`

where;

the threshold of hearing
`I_o = 10^(-12) (W/m^2)`

`(102 )/(10)= log_(10)( (I)/(10^(-12)))`

`10^(10.2) = (I)/(10^(-12))`

`I = 10^(10.2) * 10^(-12)`

I = 0.01585 W/m²

If we recall, we know remember that ;

Power = Intensity × A rea

Power = 0.01585 W/m² × 4 × 3.142 × (25 m)²

Power = 124.50 W