Question

Show your work for the following, not just the final answer:

a) What is the SIL for a sound of intensity Ia=5.2

Answer 1

Solution:

a) sound intensity level (SIL) in decibels = dB = 10 log (I a/ Io)

Ia= 5.2 x10^5 W/m^2

Io= threshold intensity level = 10^-12 W/m^2(standard value)

=> dB = 10log(5.2x10^-5/10^-12)

          = 10 log( 5.2 x10^7)

          =10 ( 7.716) = 77.2 dB

b) Ib = 3.7 x10^-7 W/m^2

dB = 10 log(Ib/Io)

c) Intensity level in decibel = dB = 10 log (intensity Ic/Io)

35 = 10 log (Ic/10^-12)

=>35/10 = log ( Ic/10^-12)

=> 3.5 = log ( Ic) - log (10^-12)

=> 3.5 = log Ic - (-12)

=>3.5-12 =log Ic

= > log Ic = - 8.5

=> Ic = 10^-8.5 = 3.16 x10^-9 W/m^2

d) given SIL = dB = 87 dB

dB = 10 log (Id/Io)

=>87 = 10 log (Id/10^-12)

=> 8.7 = log Id - log(10^-12)

=> log Id = 8.7 -12

=>Id = 10^- 3.3

=> Id = 0.00050 W/m^2

        = 5 x 10^-4 W/m^2

=> dB = 10 log(3.7 x 10^-7/10^-12)

          = 10 log ( 3.7 x10^5)

          = 10 (5.568)

         = 55.7 dB