The speed of a transverse wave passing through a string of length 50 cm and mass 10 g is 60 m s - 1 . The area of cross-section of the wire is 2 . 0 mm 2 and its Young's modulus is 1 . 2 × 10 11 N m - 2 . The extension of the wire over its natural length due to its tension will be x × 10 - 5 m . The value of x is _____ .

Step-by-step solution

The wave speed in string is given by v w = T μ , where, T is tension and μ = m l is linear mass density. Putting the values, we have ⇒ 60 = T 10 × 10 - 3 × 0 . 5 ⇒ T = 60 2 × 10 - 2 0 . 5 = 72   N The Young's modulus is given by Y = F l A ∆ l , here, A is area. From above the extension of the wire is Δ l = T l A Y = 72 × 0 . 5 2 × 10 - 6 × 1 . 2 × 10 11 = 72 × 5 24 × 10 - 5 = 15 × 10 - 5   m . Hence, the value of x = 15