Both the strings, shown in figure, are made of same material and have same cross section. The pulleys are light. The wave speed of a transverse wave in the string AB is `u_(1)` and in it is `v_(2)`. Then `v_(1)//v_(2)` is

Explanation

If `T_(1) and T_(2)` are the tensions in strings AB and CD resepctively then `T_(2)=2T_(1)`.
since `v prop sqrt(T)`
we have `(v_(1))/(v_(2))= sqrt((T_(1))/(T_(2)))`
`:.(v_(1))/(v_(2))=(1)/(sqrt(2))`