Question

The sound from a siren is radiates isotropically in air at 20oC. Five meters from the siren, the sound intensity level is 52 dB. At what distacne will the sound intensity level be 30 dB?

Answer 1

Sound intensity is given by,

here, Io = 10^-12 W/m^2

initially,L = L1 = 52 dB

and, I = I1

So, eq(1)

in second case,

L = L2 = 30 dB

I = I2

So, eq(2)

now, subtracting both equation,

52 - 30 = 10*log₁₀(I1/I2)

So, I1/I2 = 10^[(52-30)/10] = 10^2.2

also, intensity is given by,

I = P/(4*pi*r^2)

So,

then, I1/I2 = (r2/r1)^2

given, r1 = 5 m

So, r2^2 = (r1^2)*10^2.2

r2^2 = (5^2)*10^2.2

r2 = 62.95 m

Please upvote.