A wire of density `9xx10^(-3) ` kg ` cm^(-3)` is stretched between two clamps 1 m apart. The resulting strain in the wire is`4.9 xx10^(-4)` . The lowest frequency of the transverse vibrations in the wire is (Young’s modulus of wire Y= `9 xx 10^(10) "nm"^(-2)`) , (to the nearest integer), _______.

Options

A. The lowest frequency of standing wave is 35 Hz
B. The frequency of 1st overtone is 70 Hz
C. The frequency of 1st overtone is 105 Hz
D. The stress in the wire is `4.41xx10^(7)N//m^(2)`

Answer

A, B, D

Explanation

Speed of wave in wire
`V=sqrt((T)/(rhoA))=sqrt((Ydeltal)/(l)xxAxx(1)/(rhoA))=sqrt((Ydeltal)/(Jrho))`
Minimum frequency, that means fundamental mode.
`f=(V)/(lamda)=(V)/(2l)sqrt((T)/(M))=(V)/(2l)sqrt((Ydeltal)/(Jrho))=35Hz`

Stress=`(YDeltal)/(l)=9xx10^(10)xx(4.9xx10^(-4))/(1)=4.41xx10^(7)N//m^(2)`
And frequency of first overtone=70Hz.