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A brass rod (density 8.3 g//cm^(3)), 3m ...

A brass rod (density `8.3 g//cm^(3))`, 3m long is clamped at the centre. It is excited to give longitudinal vibrations and the frequency of the fundamental note is 600Hz. Calculate the velocity of sound in the rod and its Young's modulus.

Text Solution

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Here, `rho=8.3g//cm^(3)`
`=8.3xx10^(3)kg//m^(3)`
`L=3m. ` As the rod is clamped at the centre.
`:. (lambda_(r))/(2)=L or lambda_(r)=2L=2xx3=6m` Speed of sound in rod, `upsilon=vlambda_(r)`
`upsilon=600xx6=3.6xx10^(3)m//s`
As `upsilon =sqrt((Y)/(rho))`
`:. Y=upsilon^(2)rho=(3.6xx10^(3))^(2)xx8.3xx10^(3)`
`Y=10.76xx10^(10)N//m^(2)`
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