The speed of a transverse wave travelling in a wire of length 50 ~cm , cross-sectional area 1 ~mm ^2 and mass 5 ~g is 80 ~ms ⁻¹ . The Young's modulus of the material of the wire is 4 10¹¹ Nm ⁻² . The extension in the length of the wire is

Step-by-step solution

Given, length of the wire, aligned l & =50 ~cm & =5 10⁻² ~m aligned Cross-sectional area of wire, aligned A & =1 ~mm ^2 & =1 10⁻⁶ ~m ^2 aligned and mass of the wire, m=5 ~g Speed of transverse wave, v=80 ~m / s Now, speed of transverse wave given as array rlrl & & v & = T = T m l & v & = T m l array v^2= T m l Now, Young's modulus, Y= T A l l From Eqs. (i) and (ii), we get l= v^2 m A Y Putting the given values, we get gathered l= 80^2 5 10⁻³ 1 10⁻⁶ 4 10¹¹ ~m l=8 10⁻⁵ ~m gathered or So, the extension in the length o