Wave Motion Ques 1
- A copper wire is held at the two ends by rigid supports. At $30^{\circ} \mathrm{C}$, the wire is just taut, with negligible tension. Find the speed of transverse waves in this wire at $10^{\circ} \mathrm{C}$.
Given, Young modulus of copper $=1.3 \times 10^{11} \mathrm{~N} / \mathrm{m}^2$.
Coefficient of linear expansion of copper $=1.7 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}$.
Density of copper $=9 \times 10^3 \mathrm{~kg} / \mathrm{m}^3$.
(1979, 4M)
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Answer:
Correct Answer: 1.70.1 m/s
Solution:
- Tension due to thermal stresses,
$ T=Y A \alpha \cdot \Delta \theta \Rightarrow v=\sqrt{\frac{T}{\mu}} $
Here, $\mu=$ mass per unit length. $=\rho A$
$ \therefore \quad v=\sqrt{\frac{T}{\rho A}}=\sqrt{\frac{Y A \alpha \cdot \Delta \theta}{\rho A}}=\sqrt{\frac{Y \alpha \Delta \theta}{\rho}} $
Substituting the values we have,
$ \begin{aligned} v & =\sqrt{\frac{1.3 \times 10^{11} \times 1.7 \times 10^{-5} \times 20}{9 \times 10^3}} \\ & =70.1 \mathrm{~m} / \mathrm{s} \end{aligned} $
BETA
