A wire of density `9xx10^3 kg//m^3` is stretched between two clamps 1 m apart and is stretched to an extension of `4.9xx10^-4` metre.Young's modulus of material is `9xx10^10 N//m^2`.Then

Options

A. The lowest frequency of standing wave is `35 Hz`
B. The frequency of `1 st` overtone is `70 Hz`
C. The frequency of `1 st` overtone is `105 Hz`
D. The stress in the wire is `4.41 xx 10^(7) N//m^(2)`

Answer

A, B, D

Explanation

Speed of wave in wire
`V = sqrt((T)/(rho A)) = sqrt(( Y Delta l)/( l) A xx (1)/( rho A)) = sqrt(( Y Delta l)/( l rho))`
Maximum frequency , that means fundamental mode .
` f = (V)/(lambda) = (V)/(2 l) = (1)/( 2l) sqrt((Y Delta l)/( l rho)) = 35 Hz`
Stress ` = Y (Delta l)/( l)`
`= 9 xx 10^(10) xx (4.9 xx 10^(-4))/( 1)`
`= 4.41 xx 10^(7) N//m^(2)`
and frequency of first overtone ` = 70 Hz`.