Answer:

A) v/ sq. rt. of 2

Explanation:

The speed of the wave in the string is defined as:

[tex]v=\sqrt{\frac{T}{\mu}}[/tex]

Where T is the tension on the string and [tex]\mu[/tex] is the linear density, that is, the mass per unit length:

[tex]\mu=\frac{m}{L}[/tex]

Where m is the mass of the string and L its length. We have [tex]m’=2m[/tex], [tex]T’=T[/tex] and [tex]L’=L[/tex]:

[tex]v’=\sqrt\frac{T’}{m’/L’}\\v’=\sqrt\frac{T}{2m/L}\\v’=\frac{1}{\sqrt2}\sqrt\frac{T}{m/L}\\v’=\frac{v}{\sqrt2}[/tex]