One end of thin aluminium rod (cross -sectional Area `=10^(-6)m^(2)`) is bult welded to the end of copper rod with same diameter. Both rods are very long and under uniform tension of `900N` Given that
`Y_((Cu))=1.6xx10^(11)Nm^(-2), Y_((Al))=0.9xx10^(11)Nm^(-2)`
`rho_((Cu))=8.1xx10^(3)kgm^(-3), rho_((Al))=2.5xx10^(3)Kgm^(-3)`

Options

A. The value of relection factor `(A_(r))/(A_(i))` for longitudinal pulse approacing the junction along copper rod is 0.15
B. The value of reflection factor `(A_(r))/(A_(i))` for longitudinal pulse approachig the junction along copper rod is approximately 0.3
C. The value of reflection factor `(A_(r))/(A_(i))` or transverse pulse approaching the junction along copper rod is `0.15`
D. The value of reflection factor `(A_(r))/(A_(i))` for transverse pulse approaching the junction along copper rod is approximately 0.3

Answer

B, C

Explanation

For transverse wave, `v_(T)=sqrt(F/(mu))=sqrt(F/(rhoxxS))`
`V_(Al)=sqrt(900/(2.5xx10^(3)xx10^(-6)))=30/(50xx10^(-3))=600m//s`
`V_(Cu)=sqrt(900/(8.1xx10^(3)xx10^(-6)))=30/(90xx10^(3))=1000/3m//s`
`(a_(r))/(a_(i))=(V_(Al)-V_(Cu))/(V_(Al)+(V_(Cu)))=(800/3)/(2800/3)=2/7~~0.3`
For longitudinal wave `V_(l)=sqrt(Y/(rho))`
`V_(Al)=sqrt((9xx10^(10))/(2.5xx10^(3)))=(3xx10^(5))/50=6000m//s`
`V_(Cu)=sqrt((16xx10^(10))/(8.1xx10^(3)))=(4xx10^(5))/(9xx10)=40000/9m//s`
`(a_(r))/(a_(i))=(V_(Al)-V_(Cu))/(V_(Al)+V_(Cu))=(1400/9)/(94000/9)=7/47~~0.15`