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A wire of density 9xx10^3 kg//m^3 is str...

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

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)`

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
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.
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