Wave motionMediumBloom L3
Question
The speed of longitudinal wave is 100 times the speed of transverse wave in a taut brass wire. If the Young’s modulus of brass is 1.0 × 1011 N/m2, the stress in wire is
Options
A.1.0 × 107 N/m2
B.1.0 × 106 N/m2
C.1.0 × 105 N/m2
D.1.0 × 108 N/m2
Solution
Sol. Vlongitudinal = $\sqrt{\frac{Y}{\rho}}$
Vtransverse = $\sqrt{\frac{T}{\mu}}$
⇒ $\sqrt{\frac{Y}{\rho}}$ = $100\sqrt{\frac{T}{\mu}}$
⇒ $\sqrt{\frac{Y}{\mu/A}}$ = $100\sqrt{\frac{T}{\mu}}$
⇒ $\frac{10^{11}A}{\mu}$ = $10^{4}\frac{T}{\mu}$
⇒ $\frac{T}{A}$ = 107 N/m2
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