Question

If two firecrackers produce a sound level 85dB. What level does the explosion of one firecracker produce?

Answer 1

Level of sound is related to intensity by this equation

`L = 10 Log (I)/(I_o)`

given that

L = 85 dB

also we know that

`I_o = 10^(-12) W/m^2`

now we have

`85 = 10 Log (I)/(10^(-12))`

By solving above equation

`I = 10^(8.5) * 10^(-12)`

`I = 3.16 * 10^(-4) W/m^2`

now above is the intensity due to two firecrackers and if we wish to find the sound level of one firecracker then we will find its half level intensity

`I_1 = (I)/(2)`

`I_1 = 1.58 * 10^(-4)`

now again by above formula

`L = 10 Log (1.58 * 10^(-4))/(10^(-12))`

`L = 82 dB`