Answer:
The wave speed would be increased by [tex]\sqrt{2}[/tex]
Explanation:
As the formula for the wave speed of string v when subjected to tension T is:
[tex]v = \sqrt{\frac{T}{\mu}}[/tex]
where μ is the string density (mass per length), which is constant for this case.
So when a string is subjected to tension 2T then
[tex]\frac{v_2}{v} = \frac{\sqrt{2T/\mu}}{\sqrt{T/\mu}}[/tex]
[tex]\frac{v_2}{v} = \sqrt{\frac{2T}{T}\frac{\mu}{\mu}} = \sqrt{2}[/tex]
[tex]v_2 = \sqrt{2}v[/tex]
So the wave speed would be increased by [tex]\sqrt{2}[/tex]
