Question 132: Waves

Question

Speed of a transverse wave on a straight wire (mass 6.0 g, length 60 cm and area of cross-section 1.0 mm
2
) is 90 ms
-1
. If the Young's modulus of wire is 16 $$ 	imes $$ 10
11
Nm
-2
, the extension of wire over its natural length is :

Accepted Answer

Velocity of the wave, v = $$\sqrt {{T \over \mu }} $$
$$ \Rightarrow $$ T = v
2
$$\mu $$
We know, Youngs modulus,
Y = $${{{F \over A}} \over {{{\Delta l} \over l}}}$$ = $${{{T \over A}} \over {{{\Delta l} \over l}}}$$
[As here F = T]
$$ \Rightarrow $$ $${Y{{\Delta l} \over l}}$$ = $${{T \over A}}$$ = $${{{{v^2}\mu } \over A}}$$
$$ \Rightarrow $$ $$\Delta $$
l
= $${{{{v^2}\mu l} \over {AY}}}$$
= $${{90 	imes 90 	imes {{60 	imes {{10}^{ - 3}}} \over {60 	imes {{10}^{ - 2}}}} 	imes 60 	imes {{10}^{ - 2}}} \over {1 	imes {{10}^{ - 6}} 	imes 16 	imes {{10}^{11}}}}$$
= 3 $$ 	imes $$ 10
-5
m
= 0.03 mm

Answer

0.03 mm

Answer

0.04 mm

Answer

0.02 mm

Answer

0.01 mm

Waves

Speed of a transverse wave on a straight wire (mass 6.0 g, length 60 cm and area of cross-section 1.0 mm 2 ) is 90 ms -1 . If the Young's modulus of wire is 16 $ \times $ 10 11 Nm -2 , the extension of wire over its natural length is :

Choose the correct answer: