(a) Sound with intensity larger than `120 dB` appears painful to a person. A small speaker delivers `2.0 W` of audio output. How close can the person get to the speaker without hurting his ears?
(b) If the sound level in a room is increased from `50 dB` to `60 dB`, by what factor level is the pressure amplitude increased?

Explanation

(a) `L = 10 log_(10)((I)/(I_ (0)))`
`120 = 10 log_(10)((I)/(10^(-12)))`
`(I)/(10^(12)) = 10^(12) rArr I = 1 W//m^(2)`
For a point source of power `P`, intensity at distance `r`
`I = (P)/(4pi r^(2))`
`r = sqrt ((P)/(4pi I)) = sqrt ((2)/(4pi xx 1)) = sqrt ((1)/(2pi)) = 0.4 m`
(b) `L_(2) - L_(1) = 10 log_(10)(I_(2)/(I_(1)))`
`60 - 50 = 10 log_(10)(I_(2)/(I_(1))) rArr log_(10)(I_(2)/(I_(1))) = 1`
`I_(2)/(I_(1)) = 10`
`I prop p_(0)^(2)`
`I_(2)/(I_(1)) = [(p_(0))_(2)^(2)/(p_(0))_(1)^(2)] = 10`
`(p_(0))_(2)/(p_(0))_(1) = sqrt (10)`