Question

An audio system 1 produces a sound level of 90.0 dB and system 2 produces a sound level of 93.0 dB. (a) Determine the ratio of the intensities (in W/m2). (b) Suppose a recording device was placed 2 m away from system 2. How far away from system 1 must that recording device be placed in order for the intensity to be the same as it was near system 2?

Answer 1

here,

intensity ratio is given by expression,

(dB2 - dB1) = log(I2/I1)
I2/I1 = 10^(dB2 - dB1)
I2/I1 = 10^(93 - 90)
I2/I1 = 10^0.3
I2/I1 = 2 --------------(1)

Part b:
Intensity variation with distance is given as:

I1/I2 = r2^2/r1^2

From Question, r2 = 2 m , also from eqn 1 I2/I1 = 2

Solving for distance from first source, r1 = sqrt((I2/I1)*r2^2)
r1 = sqrt((2)*(2)^2)
r1 = 2.83 m