A chinese fire cracker when busted creates 100 dB sound at a distance of 10 cm. this level of sound is dangerous and can create deafness. To reduce the sound to a safer level, we need to stand far from it. At what minimum destance from the fire cracker a person should stand so that sound level heard by him is 40 dB? (Assume that sound energy spread equally in all directions)

Options

A. 100 m
B. 6.63 cm
C. 10 m
D. 1 m

Answer

A

Explanation

Intensity at 10 cm
`100=10log(I_(1))/(I_(0))`
`impliesI_(1)=10^(-2)=W//m^(2)`
Intensity at `r` distance
`40=10log(I_(2))/(I_(0))`
`impliesI_(2)=10^(-8)W//m^(2)`
Since firecracker is a point source:
`(I_(1))/(I_(2))=(r_(2)^(2))/(r_(1)^(2))=(r^(2))/((0.1)^(2))`
`r=0.1xxsqrt((10^(-2))/(10^(-8)))=100m`