Answer:
[tex]\frac{1}{\sqrt{2}}[/tex]
Explanation:
The speed of a wave in a string is given by:
[tex]v=\sqrt{\frac{T}{m/L}}[/tex]
where
T is the tension in the string
m is the mass of the string
L is the length
In this problem, the mass of the string is increased to 2m: m' = 2 m, while the length is not changed, L'=L. If the tension in the string is not changed, then the new speed of the wave in the string will be:
[tex]v'=\sqrt{\frac{T}{m'/L'}}=\sqrt{\frac{T}{2m/L}}=\frac{1}{\sqrt{2}}\sqrt{\frac{T}{m/L}}=\frac{v}{\sqrt{2}}[/tex]
so, the speed of the wave decreases by a factor [tex]\frac{1}{\sqrt{2}}[/tex]
