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

Answer

A, B

Explanation

Speed of wave in wire
`V=sqrt((T)/(rhoA))=sqrt((Y Delta l)/(l)xx(1)/(rhoA))=sqrt((Y Delta l)/(l rho))`
Maximum time period means minimum frequency , that means fundamental mode
`f=(V)/(lamda)=(V)/(2l)`
`:. T = (2l)/(V)=2lsqrt((l rho)/(Y Delta l)) = (1)/(35)sec`
`:. (f=35 Hz)`
and frequency of first overtone
`=(V)/(l)=70Hz`