The correct option is: (b) L/√2
Explanation:
The Fundamental is given by
and the velocity is given by
2x the density means 2x the m/L so that the velocity of the second string is smaller compared to the first string by v2 = v1 / √2. The first string length is L1 = 2f/v1, the second string length is L2 = 2f/(v1 / √2). So comparing the two we have L2 = L1 / √2