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. 105 Hz
B. 70 Hz
C. 35 Hz
D. 15 Hz

Answer

C

Explanation

For the stretched wire ` n = 1/(2L) sqrt(T/m) `
` :' Y = (MgL)/(Al) " and " Mg = T :. T = (YAl)/L `
and ` "mass"/"length" = (vrho)/L = (ALrho)/L = Arho`
` :. n = 1/(2L) sqrt(T/m) `
` = 1/(2L) sqrt((YAl)/L xx 1/(Arho)) = 1/(2L) sqrt((Yl)/(Lrho)) `
` = 1/(2 xx 1) sqrt((9 xx 10^(10) xx 4.9 xx 10^(-4))/(1 xx 9 xx 10^(3))) `
` :. n = 1/2 sqrt(49 xx 10^(2))`
` :. n = 35` Hz