A wire stretched between two rigid supports vibrates in tits fndamental mode with a frequency of 45 Hz. The mass of the wire is `3.5 xx 10 ^(-2) kg and ` its inear mass density is `4.0 xx 10 ^(-2) kg m ^(-1).` What is (a) the speed oa a transverse wave on the string, and (b) the tension in the string ?

Explanation

(a) Fundamental frequency of stationary wave,
`f _(1) = (v)/(2L) implies f _(1) = (v mu)/(2 xx M)`
`(because mu = (M)/(L) implies L = (M)/(mu)) `
`therefore v =(2f _(1) M )/( mu) = (2 xx 45 xx 0.035)/(0.04) = 78.75 (m)/(s)`
(b) Wave speed of transverse wave,
`v = sqrt ((T)/(mu))`
`therefore v ^(2) = (T)/(mu) implies T = muv ^(2)`
`therefore T = (0.04) (78,75)^(2) = 248.1 N`