A steel wire of length ` 1 m` and density `8000 kg//m^(3)` is stretched tightly between two rigid supports . When vibrating in its fundamental mode , its frequency is `200 Hz`.
a. What is the velocity of transverse wave along this wire ?
b. What is the longitudinal stress in the wire ?
c. If the maximum acceleration of the wire is `880 m//s^(2)`, what is the amplitude of vibration at the midpoint ?

Explanation

`a. n_(0) = ( c)/( 2I) or c = 2 n_(0)I`
`:. C = 2 xx 200 xx 1 = 400 m//s`
b. ` c = sqrt ((T)/(m)) = sqrt (( pi r^(2) xx stress)/( pi r^(2) xx density)) = sqrt((stress)/( density))`
`:. Stress = c^(2) rho = 400^(2) xx 8000 = 1.28 xx 10^(9) N//m^(2)`
c. Acceleration ` = - omega^(2) xx displacement`
`:. 800 = (2 pi n)^(2) xx a where a = amplitude`
or `a = (800)/((2 pi xx 200)) = 5 xx 10^(-4) m`