Speed of a transverse wave on a straight wire (mass 6.0 g, length 60 cm and area of cross-section 1.0 mm2) is 90 ms-1. If the Young's modulus of wire is 16 $\times$ 1011 Nm-2, the extension of wire over its natural length is :
Solution
Velocity of the wave, v = $\sqrt {{T \over \mu }}$
<br><br>$\Rightarrow$ T = v<sup>2</sup>$\mu$
<br><br>We know, Youngs modulus, <br><br>Y = ${{{F \over A}} \over {{{\Delta l} \over l}}}$ = ${{{T \over A}} \over {{{\Delta l} \over l}}}$
<br><br>[As here F = T]
<br><br>$\Rightarrow$ ${Y{{\Delta l} \over l}}$ = ${{T \over A}}$ = ${{{{v^2}\mu } \over A}}$
<br><br>$\Rightarrow$ $\Delta$<i>l</i> = ${{{{v^2}\mu l} \over {AY}}}$
<br><br>= $${{90 \times 90 \times {{60 \times {{10}^{ - 3}}} \over {60 \times {{10}^{ - 2}}}} \times 60 \times {{10}^{ - 2}}} \over {1 \times {{10}^{ - 6}} \times 16 \times {{10}^{11}}}}$$
<br><br>= 3 $\times$ 10<sup>-5</sup> m
<br><br> = 0.03 mm
About this question
Subject: Physics · Chapter: Waves · Topic: Wave Motion and Types
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