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

Length of the rod `=lambda_(r)/2=1m=100cm`
Distance betweem consecutive heaps `=lambda_(g)/2=8cm`
`lambda_(r)/lambda_(g)=(100)/8=12.5`
Let `v_(r) and v_(g)` be the velocity of sound in the rod and the gas respectively.
`v_(r)/v_(g)=(lambda_(r))/(lambda_(g)), v_(r)=lambda_(r)/lambda_(g) v_(g)=12.5 xx 400=500m//s`
`v_(r)=sqrt(Y/p) , Y =pv_(r)^2=7.5 xx 10^(3) xx (5000)^2=1.875 xx 10^(11)N//m^2`