Question

(i) In a travelling sinusoidal longitudinal wave, the displacement of particle of medium is represented by `s = S (x, t)`. The midpoint of a compression zone and an adjacent rarefaction zone are represented by letter ‘C’ and ‘R’ respectively. The difference in pressure at ‘C’ and ‘R’ is `DeltaP` and the bulk modulus of the medium is B.
(a) How is `|(del s)/(del x)|` related to `|del/del|`
(b) Write the value of `|(del s)/(del x)|_(C)` in terms of `DeltaP` and `B`.
(c) What is speed of a medium particle located mid-way between ‘C’ and ‘R’.
(ii) A standing wave in a pipe with a length of `L = 3 m` is described by `s=A cos ((3pi x)/(L)) sin ((3pi vt)/(L))` where `v` is wave speed. The atmospheric pressure and density are `P_(0)` and `rho` respectively.
(a) At `t=L/(18v)` the acoustic pressure at `x =L/2` is `0.2` percent of the atmospheric pressure . Find the displacement amplitude A.
(b) In which overtone is the pipe oscillating?

Answer 1

Correct Answer - (i) (a) `|(del S)/(del x)|_(C)= |(del S)/(del x)|_(R)`
(b) `|(del S)/(del x)|_(C)=(Delta P)/(2B)`
(C) Zero
(ii) (a) `(0.0004LP_(0))/(3piv^(2) rho)`
(b) Second