Question 298: Properties of Matter

Question

A wire of density 9 $$ 	imes $$ 10–3 kg cm–3 is stretched
between two clamps 1 m apart. The resulting
strain in the wire is 4.9 $$ 	imes $$ 10–4. The lowest
frequency of the transverse vibrations in the
wire is : (Young’s modulus of wire Y = 9 $$ 	imes $$ 1010
Nm–2), (to the nearest integer), _________

Accepted Answer

$$ho $$
wire
= 9 $$ 	imes $$ 10
Ã¢ÂÂ3
kg cm
Ã¢ÂÂ3
= $${{9 	imes {{10}^{ - 3}}} \over {{{10}^{ - 6}}}}$$ kg/m
3
= 9000 kg/m
2
f = $${1 \over {2l}}\sqrt {{T \over \mu }}  = $$$${1 \over {2l}}\sqrt {{T \over {{ho _{wire}}A}}} $$
= $${1 \over {2l}}\sqrt {{{Y\Delta l} \over {{ho _{wire}} A}}} $$
$$ = {1 \over {2 	imes 1}}\sqrt {{{9 	imes {{10}^{10}} 	imes 4.9 	imes {{10}^{ - 4}}} \over {9000 	imes 1}}} $$
= 35 Hz

Properties of Matter

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