When the area of cross-section of a stretched wire is halved and tension is doubled, the speed of propagation of transverse waves along it becomes k times the initial speed. Then, k

Step-by-step solution

Speed of transverse wave in stretched wire is given as v= T m where, T= tension in the wire and m= mass per unit length of wire. aligned & v= T M / l [ m= M l ] & = T l M = T l V & [ M=V ] & = T l A l & [ V=A l] & v= T A v T A & v₂ v₁ = T₂ T₁ A₁ A₂ & Given, A₂= A₁ 2 , T₂=2 T₁ & aligned From Eq. (i), we get aligned & v₂ v₁ = 2 T₁ T₁ A₁ A₁ 2 = 4 & v₂=2 v₁ K=2 aligned