Answer :
The wave speed on a taut string is
v = √(T/μ)
where T is the tension and μ the mass per unit length of the string.
Therefore, to double the wave speed on the string, the tension has to increase by a factor of 4.
In your notation
v = √(T/μ)
where T is the tension and μ the mass per unit length of the string.
Therefore, to double the wave speed on the string, the tension has to increase by a factor of 4.
In your notation