A wire of density `9 xx 10^(3) kg//m^(3)` is stretched between two clamps 1 m apart and is subjected to an extension of `4.9 xx 10^(-4) m`. The lowest frequency of transverse vibration in the wire is `(Y = 9 xx 10^(10) N//m^(2))`

Options

A. 40 Hz
B. 35 Hz
C. 30 Hz
D. 25 Hz

Answer

B

Explanation

Given : `I = 4.9 xx 10 ^( -4) ` m
From the formula
` Y = ("stress")/("strain") = ( F//pi r^2 )/( I//L ) or ( F)/( pi r^ 2 ) = Y ( I)/(L ) `
` = 9 xx 10 ^( 10 ) xx ( 4.9 xx 10^( -4 ) ) /( 1 ) = 44.1 xx 10 ^( 6 ) `
` v = ( 1 ) /( 2L ) sqrt (( ( T)/(m))) = ( 1 ) /( 2L ) sqrt ((( F)/(pi r ^ 2 d ))) `
` = ( 1 )/ ( 2 ) sqrt(((F//pi r ^2 )/(d))) = ( 1 )/( 2 ) xx sqrt (((44.1 xx 10^( 6))/( 9 xx 10 ^ 3 ))) `
` = ( 1 ) /( 2 ) sqrt( ( 4.9 xx 10^ 3 )) = ( 1 ) /( 2 ) sqrt (( 49 xx 10 ^ 2 )) `
` = ( 7 xx 10 ) /( 2 ) = 35 `Hz