A copper wire 2.4 mm in diameter is 3m long and is used to suspend an 8kg mass from a beam. If a transverse disturbance is sent along the wire by striking it lightly with a pencil, how fast will the disturbance travel? The density of copper is $8920 k g / m^{3}$ . [Assuming tension to be constant in the wire and equal to tension at the lower end]

40.2 m/s

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425 m/s

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44.5 m/s

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15.6 m/s

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Solution

The correct option is C 44.5 m/s
Tension, $T = 8 \times 10 = 80 N$
Radius of wire, $r = 1.2 \times 10^{- 3} m$
Velocity of transverse wave, $v = \sqrt{\frac{T}{ρ A}} = \sqrt{\frac{80}{8920 \times π \times (1.2 \times 10^{- 3})^{2}}} = 44.5 m / s$

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The correct option is C 44.5 m/sTension, T=8×10=80 N Radius of wire, r=1.2×10−3 m Velocity of transverse wave, v=√TρA=√808920×π×(1.2×10−3)2=44.5 m/s

The correct option is C 44.5 m/s
Tension, $T = 8 \times 10 = 80 N$
Radius of wire, $r = 1.2 \times 10^{- 3} m$
Velocity of transverse wave, $v = \sqrt{\frac{T}{ρ A}} = \sqrt{\frac{80}{8920 \times π \times (1.2 \times 10^{- 3})^{2}}} = 44.5 m / s$