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Q.

A copper wire is held at the two ends by rigid supports. At $30^{0}$ the wire is just taut with negligible tension. The speed of transverse waves in this wire at $10^{0} C$ is $10 \times D m / s .$ Find the value of D(Take, $Y_{c u} = 1.3 \times 10^{11} P a,$ $α_{c u} 1.7 \times 10^{- 5} /^{0} C, ρ_{c u} = 9000 k g / m^{3}$ )

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answer is 7.

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Detailed Solution

Thermal stress $= \frac{F}{A} = y α Δ θ,$ where $F$ is tension and $A$ is area or cross-section.
We known, $v = \sqrt{\frac{F}{ρ A}} = \sqrt{\frac{T h e r m a l s t r e s s}{D e n s i t y}} = \sqrt{\frac{Y α Δ θ}{ρ}}$
$= \sqrt{\frac{1.3 \times 10^{11} \times 1.7 \times 10^{- 5} \times (30 - 10)}{9000}} = 70 m s^{- 1}$
$∴ D = 7$

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A copper wire is held at the two ends by rigid supports. At 300 the wire is just taut with negligible tension. The speed of transverse waves in this wire at 100C is 10×Dm/s. Find the value of D(Take, Ycu=1.3×1011 Pa, αcu1.7×10−5 / 0C, ρcu=9000 kg/ m3)