Two uniform strings A and B made of the same material have lengths in the ratio 1:3 and diameters in the ratio 2:1 . If they are subjected to identical tension, what is the ratio of the speeds of transverse waves in string A to that in string B?

Step-by-step solution

The speed of a transverse wave in a string is given by v = T , where T is the tension and is the linear mass density. The linear mass density can be expressed as = A = D^2 4 , where is the density of the material and D is the diameter of the string. Since both strings are made of the same material and subjected to identical tension, T and are the same for both strings. Thus, the speed of the transverse wave is inversely proportional to the diameter of the string, v 1 D . The ratio of the speeds of transverse waves