(i) In a travelling sinusoidal longitudinal wave, the displacement of particle of medium is
Channel: Doubtnut
Date: 16/02/2020

(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?