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

$L = 10 Log \frac{I}{I_o}$

given that

L = 85 dB

also we know that

$I_o = 10^{-12} W/m^2$

now we have

$85 = 10 Log \frac{I}{10^{-12}}$

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

$I_1 = \frac{I}{2}$

$I_1 = 1.58 * 10^{-4}$

now again by above formula

$L = 10 Log \frac{1.58 * 10^{-4}}{10^{-12}}$

$L = 82 dB$