Final answer:
The speed of transverse waves on a string is inversely proportional to the square root of the linear mass density. Since string A has a cross-sectional radius that is double that of string B, its linear mass density is four times greater, halving its wave speed compared to string B. Therefore, the ratio of VA to VB is 1/2.
Step-by-step explanation:
The question deals with the comparison of wave speeds in two strings of different cross-sectional radii stretched with the same tension. The speed of transverse waves on a string (v) is derived from the formula v = √(T/μ), where T is the tension and μ is the linear mass density. Since both strings A and B are made of the same material and stretched by the same tension, T is constant for both strings.
If the radius is doubled, the cross-sectional area becomes four times larger (since the area is proportional to the square of the radius) therefore, making the linear mass density of string A four times that of string B given the mass is distributed over the length of the string which remains the same. As a result, the speed of wave on string A (VA) will be halved compared to string B (VB), because the wave speed is inversely proportional to the square root of the linear mass density. Hence, the ratio VA/VB is 1/2.