A copper wire 2.4 mm in diameter is 3 m long and is used to suspend a 2 kg 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 $8920 k g / m^{3}$

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Solution

Speed of transverse disturbance in a wire= $\sqrt{\frac{T}{μ}}$
where $T$ is tension in the string, $μ$ is the mass per unit length of the wire.
$μ = \frac{m}{l} = \frac{ρ A l}{l} = ρ A$
A is the cross sectional area.
Thus $v = \sqrt{\frac{2 \times 9.8}{8920 \times π \times {0.0012}^{2}}} = 22 m / s$

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A copper wire 2.4 mm in diameter is 3 m long and is used to suspend a 2 kg 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 8920kg/m3

Speed of transverse disturbance in a wire=√Tμwhere T is tension in the string, μ is the mass per unit length of the wire.μ=ml=ρAll=ρAA is the cross sectional area.Thus v=√2×9.88920×π×0.00122=22m/s

A copper wire 2.4 mm in diameter is 3 m long and is used to suspend a 2 kg 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 $8920 k g / m^{3}$