A metallic rod of length 1 m is rigidly clamped at its midpoint. Longitudinal stationary waves are set up in the rod in such a way that there are two nodes on either side of the midpoint. The amplitude of an antinode is `2xx10^(-6)m`.
(i) Write the equation of motion at a point 2 cm from the midpoint __________ (ii) Write the equation of constituent waves in the rod _________ `(Y=2xx10^(11)N//m^(2) and rho=8xx10^(3)kg//m^(3))`.

Answer

`y(x,t) = 2 xx 10^(-8)sin6pix cos(6sqrt(30) pi xx 10^(3)t + theta)`
at `x = 0.1`
`y(0.1,t) = 2 xx 10^(-6)sin'(6pi)/(10)cos`
`(6sqrt(30)pi xx 10^(3)t + theta)`
`y_(1), (x,t) = 1 xx 10^(-6)sin`
`(6pix + 6sqrt(30)pi xx 10^(3)t + theta_(1))`
`y_(2) (x,t) = 1 xx 10^(-6)sin`
`(6pix - 6sqrt(30)pi xx 10^(3)t + theta_(2))`
at `x = 0.1`
`y_(1) = (0.1,t) = 1 xx 10^(-6)sin`
`((6pi)/(10) + sqrt(30)pi xx 10^(3)t + theta_(1))`
`y_(2)(0.1,t) = 1 xx 10^(-6)sin`
`((6pi)/(10) - 6sqrt(30)pi xx 10^(3)t + theta_(2))`