At a certain distance from a blaring speaker you measure the

At a certain distance from a blaring speaker, you measure the sound level to be just 98.3 dB. You walk 3.00 m further away from the speaker and measure the sound level to be just 86.3 dB. Determine the intensity (in W/m^2) at these two locations. b. Determine the power output of speaker. c. Determine the two actual distances from the speaker.

Solution

Solution

7. a) Intensity at point where loss is 98.3dB,

I = 10^98.3/10*I_o = 10^9.83*10^-12 = 10^-2.17= 6.76*10^-3 W/m²

Intensity at point where loss is 86.3dB,

I\' = 10^86.3/10*I_o = 10^8.63*10^-12 = 10^-3.37= 4.26*10-4 W/m²

b) Here distance between two points is 3.0 m.

Let r and (r+3) be actual distance of the points from speaker.

then,

P/(4r²) = I ............1)

and, P/(4(r+3)²)= I\' .............2)

from 1) and 2)

(r+3)²/r²= I/I\' = 6.76*10^-3 /( 4.26*10^-4 )

(r+3)/r= 4

or, r=1 m

power of speaker, P = I*4r² = 8.38*10^-2 W

c) actual distances, r= 1 m and (r+3)= 4 m