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A metallic rod of length 1m is rigidly c...

A metallic rod of length 1m is rigidly clamped at its mid point. Longirudinal stationary wave are setup in the rod in such a way that there are two nodes on either side of the midpoint. The amplitude of an antinode is `2 xx 10^(-6) m`. Write the equation of motion of a point 2 cm from the midpoint and those of the constituent waves in the rod, (Young,s modulus of the material of the rod `= 2 xx 10^(11) Nm^(-2)` , density `= 8000 kg-m^(-3)`). Both ends are free.

Text Solution

Verified by Experts

The correct Answer is:
`y=10^(-6)sin(0.1pit)sin(25000pit),y_(1)=10^(-6)sin(25000pit-5pit),y_(2)=10^(-6)sin(25000 pit+5 pi x)`]
`v=sqrt((Y)/(rho))=sqrt((2xx10^(11))/(8000))=5000m//s`
`(5)/(2)lamda =LrArr lamda=(2L)/(5)=(2xx1)/(5)=0.4m`.
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