For a solid rod, the Young’s modulus of elasticity is 3.2 x1011 Nm-2 and density is 8×103 kgm-1. The velocity of longitudinal wave in the rod will be
Question
For a solid rod, the Young’s modulus of elasticity is 3.2 x 10^11 Nm^-2 and density is 8 x 10^3 kgm^-3. The velocity of longitudinal wave in the rod will be
Solution
The velocity of a longitudinal wave (v) in a solid medium can be calculated using the formula:
v = sqrt(E/ρ)
where: E is the Young's modulus of elasticity, and ρ is the density of the medium.
Given that E = 3.2 x 10^11 Nm^-2 and ρ = 8 x 10^3 kgm^-3, we can substitute these values into the formula:
v = sqrt((3.2 x 10^11 Nm^-2) / (8 x 10^3 kgm^-3))
Solving this gives:
v = sqrt(4 x 10^7 m^2s^-2)
Therefore, the velocity of the longitudinal wave in the rod is 2 x 10^4 ms^-1.
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