The faintest sound that can be heard has a pressure ampulitude of about `2 xx 10^(-5) N//m^(2)` and the loudest that can be heard without pain has a pressure ampulited of about `28 N//m^(2)`. Dentermine in each (a) the intensity of the sound both in `w//m^(2)` and in `dB` and (b) the ampulited of the oscillations if the frequency is `500 H_(Z)`. Assume an air density of `1.29 kg//m^(3)` and a velocity of sound is `345 m//s`.

Answer

A, B, C, D

Explanation

`I = (nu(Deltap)^(2)max)/(2B)`
`= ((Deltap)^(2)max)/(2B)`
For finest sound,
`I = (2 xx 10^(-5))^(2)/(2 xx 129 xx 345)`
`= 4.49 xx 10^(-13) W//m^(2)`
`L = 10 log ((I)/(I_(0)))`
`= 10 log_(10) ((4.49 xx 10^(-13))/(10^(-12)))`
`= - 3.48 dB`
Same formulae can be applied for loudest sound.
(b) `(Delta p)_(max) = BAK`
`= (rho nu)^(2) (A) ((omega)/(nu))`
`= 2 pi f rho nu`
:. `A = (Deltap)_(max)/(2 pi f rho nu)`
For finest sound,
`A = (2 xx 10^(-5))/((2 pi)(500)(1.29)(345)`
`= 1.43 xx 10^(-11) m`