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Two rods AB and BC of equal cross-sectio...

Two rods `AB` and `BC` of equal cross-sectional area are joined together and clamped between two fixed supports as shown in the figure. For the rod `AB` and road `BC` lengths are `l_(1)` and `l_(2)` coefficient of linear expansion are `alpha_(1)` and `alpha_(2)`, young's modulus are `Y_(1)` and `Y_(2)`, densities are `rho_(1)` and `rho_(2)` respectively. Now the temperature of the compound rod is increased by `theta`. Assume of that there is no significant change in the lengths of rod due to heating. then the time taken by transverse wave pulse to travel from end `A` to other end `C` of the compound rod is directly proportional to

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