(a) what is the displacemant amplitude for a sound wave having a frequency of `100 Hz` and a pressure amplitude of `10` pa? (b) The displacement amplitude of a sound wave of frequency `300 Hz` is `10^(-7)` m. what is the pressure amplitude of this wave ? speed of sound in airb is `340` ml s and density of a ir is `1.29kg// m^(3)`.

Answer

A, B, C

Explanation

(a) `(Deltap)_(m) = BAk`
Here, `k = (omega)/(nu)=(2pif)/(nu)`
and `B =rho nu^(2)` `(as nu = sqrt(B/rho))`
`:. (Deltap)_(m) =(rho nu ^(2)) (A) ((2pif)/(nu))`
`:. A = (Deltap) _(m)/(2pi nu rho f)` ..(i) substituting the values, we have
`A=(10)/(2xx 3.14 xx 340xx 1.29xx 100)`
`= 3.63 xx 10 ^(-5) m`
(b) From Eq. (i) `(Deltap)_(m) = 2pi f rho nu A` substituting the values, we have
`(Delta p)_(m) = 2xx3.14 xx 300 xx 1.29 xx 340xx 10^(-7)`
`8.26 xx 10 ^(-2) N// m^(2)`