n waves are produced on a string in 1 s. When the radius of the string is doubled and the tension is maintained the same, the number of waves produced in 1 s for the same harmonic will be

Given that the frequency of wave produced in the string is 1/n.1n=12πTm. Now     T' = 2T Therefore, new frequency is f=12π2Tm=2×1nTherefore, the number of waves produced per second is 1f=n2