Question

Subwoofer Speaker Review A subwoofer is a type of speaker designed to emit low-frequency sound waves. Suppose a subwoofer is attached to a vertical pole. Of all the energy this subwoofer generates, 75 % of it is emitted forward in front of the suboofer, and 25 % is emitted backwards behind the subwoofer. Suppose a student takes a sound sensor and stands 1.0 m in front of the subwooferand 2.5 m below it. He measures a sound intensity level of 85 dB on his meter while standing at this point.

Answer 1

(1) Intensity follows the $1/(r^{2})$ law.

where r is the distance from the origin of the sound waves.

The distance of measurement is given by the pythagoras theorem : $r^{2} = (1)^{2} + (2.5)^{2}$

r = 2.69 m

Intensity is given in decibel level, conversion into watts : I (db) = 10*log(I'/Io)

where I' is the intensity in Watts/m^2

and Io is the reference intensity Io =  $10^{-12}$ Watts/m^2

thus 85 db in Watts/m^2 is I = 0.000316 Watt/m^2

Let the intensity in the forward direction be $I_{f}$ ,

I =   $I_{f}$ / r^2

  $I_{f}$ = I * r^2

$I_{f}$ = 0.000316*2.69*2.69

$I_{f}$ = 0.0023 Watts/m^2

which is just the 75% of the Intensity, total intensity emmitted is

I_total =  $I_{f}$ /0.75 = 0.00305 Watts/m^2 = 94.85 db.