First slide

Travelling wave

Question

Speed of a transverse wave on a straight wire (mass 6.0g, length 60 cm) and area of cross-section of wire $(1.0 m m^{2})$ is $80 m / \sec$ . If the young’s modulus of wire is $16 \times 10^{11} N / m^{2}$ , then extension of wire over its natural length is

Moderate

A

0.02 mm
B

0.04 mm
C

0.03 mm
D

0.024 mm

Solution

$v = \sqrt{\frac{T}{μ}} \Rightarrow V = \sqrt{\frac{\frac{Y A Δ l}{l}}{\frac{m}{l}}} = \sqrt{\frac{16 \times 10^{11} \times 1 \times 10^{- 6} \times Δ l}{6 \times 10^{- 3}}} \Rightarrow 80 = \sqrt{\frac{16 \times 10^{11} \times 1 \times 10^{- 6} \times Δ l}{6 \times 10^{- 3}}} \Rightarrow 64 \times 10^{2} = \frac{16 \times 10^{5}}{6 \times 10^{- 3}} \times Δ l \Rightarrow Δ l = 0.024 m m$

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