Clamped at the middle a metal rod of length 1m and density `7.5 xx 10^(3)kg//m^3` gives dust heaps at intervals of 8cm. Calculate the Young's modulus of the material of the rod. Velocity of sound in the gas used in 400m/s.

Explanation

Velocity of sound in the rod `=V_(r)=?`
Velocity of sound in the gas `=V_(g)=400m//s`
Length of the rod `=l_(r)=1m`
Density of the rod `=p_(r)=7.5 xx 10^(3) "kg/m"^3`
Average distance between two consecutive dust-heaps in the gas
`l_(g)=8cm =0.08m`
`V_r/V_g=(lambda_(r))/(lambda_(g))=(2nI_(r))/(2nl_(g))`
`V_(r)=(l_(r))/(l_(g)) xx V_(g)=1/(0.08) xx 400`
=5000m/s
`V_(r)=sqrt((Y)/(p_(r))`
`Y=V_(r)^2 p_(r)=(5000)^2 xx 7.5 xx 10^(3)`
`=1.87xx10^(11) N//m^2`