(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?

(i) In a travelling sinusoidal longitudinal wave, the displacement of

1.	(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» 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

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