Answer each of the following questions related to Sound Inte

Answer each of the following questions related to Sound Intensity and Sound Intensity Level (SIL): (a). A sound has an intensity of 10^-7 W/m^2. What is its SIL? (b). A total of seven sound sources produce the same intensity of sound as that given in part (a). What is the total SIL that they produce? (c). What is the sound intensity of an 80dB sound? (d). You hear a sound with SIL of 90dB. If you move to a position twice as far from the sound source what SIL will you hear? Assume that the sound travels out equally in all directions from the source (i.e. it is isotropic).

Solution

(a). Intensity I = 10 ^-7 W/m ²

Sound intensity level L = 10 log ₁₀ ( I / Io)

Where Io = reference intensity = 10 ^-12 W/m ²

Substitute values you get , L = 10 log ₁₀ (10 ^-7 / 10 ^-12 )

                                           = 10 log ₁₀ (10 ⁵)

                                           = 10 ( 5 )

                                           = 50 dB

(b).Total intensity I \' = 7 I = 7 x10 ^-7 W/m ²

Sound intensity level L \' = 10 log ₁₀ ( I \' / Io)

Where Io = reference intensity = 10 ^-12 W/m ²

Substitute values you get , L = 10 log ₁₀ (7 x10 ^-7 / 10 ^-12 )

                                           = 10 log ₁₀ (7x10 ⁵)

                                           = 10 ( 5.845 )

                                           = 58.45 dB

(c).Given L \" = 80 dB

Sound intensity level L\" = 10 log ₁₀ ( I\" / Io)

Where Io = reference intensity = 10 ^-12 W/m ²

Substitute values you get , 80 = 10 log ₁₀ (I \"/ 10 ^-12 )

                                         8 = log ₁₀ (I \" /10 ^-12)

                 (I \" /10 ^-12) = 10 ⁸

                                       I \" = 10 ⁸ x 10 ^-12

                                           = 10 ^-4 W/m ²

(d).Given L \" = 90 dB

Sound intensity level L\" = 10 log ₁₀ ( I\" / Io)

Where Io = reference intensity = 10 ^-12 W/m ²

Substitute values you get , 90 = 10 log ₁₀ (I \"/ 10 ^-12 )

                                         9 = log ₁₀ (I \" /10 ^-12)

                 (I \" /10 ^-12) = 10 ⁹

                                       I \" = 10 ⁹ x 10 ^-12

                                           = 10 ^-3 W/m ²

We know Intensity is inversely proportional to square of the distance.

i.e., I\" /I \"\' = r\"\' ² /r\" ²

Given r \"\' = 2r\"

I \" / I \"\' = (2r\") ² / r\" ² = 4

So, intensity at twice as far from the sound source I \"\' = I\" / 4

I\"\' = 0.25 x10 ^-3 W/m ²

Required intensity level L\"\'= 10 log ₁₀ ( I \'\" / Io)

Where Io = reference intensity = 10 ^-12 W/m ²

Substitute values you get , L\"\' = 10 log ₁₀ (0.25 x10 ^-3 / 10 ^-12 )

                                           = 10 log ₁₀ (0.25x10 ⁹)

                                           = 10 ( 8.397 )

                                           = 83.97 dB