(a) A longitudinal wave propagating in a water-filled pipe has intensity `3.00xx10^(-6) W//m ^(2)` and frequency `3400 H_(Z)` . Find the amplitude `A` and wavelength `lambda` of the wave . Water has density `1000 kg//m ^(3)` and bulk modulus `2.18xx10^(9) Pa`. (b) If the pipe is filled with air at pressure `1.00 xx10^(5)` Pa and density `1.20 kg//m^(3)`, What will be the amplitude `A` and wavelength `lambda` of a longitudinal wave the same intensity and frequency as in part (a) ? (c ) In which fluid is the amplitude larger, water or air? What is the ratio of the two amplitude ? Why is this ratio so different from/ Conider air as diatomic.

Answer

A, B, C, D

Explanation

(a) `nu = sqrt((B)/(rho)) = sqrt((2.18 xx 10^(9))/(1000))`
`= 1476 m//s`
`lambda = (nu)/(f) = (1476)/(3400) = 0.43 m`
`I = (1)/(2) rho omega ^(2) A^(2) nu`
`:. A = sqrt((2l)/(rho (2pi f)^(2) nu)`
`= sqrt((2 xx3 xx10^(-6))/((1000) (2pixx3400)^(2)(1476)))`
`= 9.44 xx10^(-11) m`
(b) `nu = sqrt((gamma P)/(rho)) = sqrt(((1.4) (10^(5)))/((1.2)))`
`= 341.56 m//s`
`lambda = (nu)/(f) = (341.56)/(3400) = 0.1 m`
`A = sqrt ((2l)/(rho (2 pi f)^(2) nu))`
`= sqrt((2 xx3.0 xx10^(-6))/(1.2xx (2pixx3400)^(2)(341.56)))`
(c) `(A_(air))/(A_(water)) = (5.66 xx 10^(-9))/(9.44 x10^(-11)) = 60`
`I = (1)/(2) rho omega^(2) A^(2) nu`
`rho` and `nu` are less in air . So , for same intensity `A` should be large.