$1$
$2$
$\sqrt{2}$
$\frac{1}{\sqrt{2}}.$
$\frac{1}{\sqrt{2}}$
Explanation:
TAB = T
TCD = 2T
where
TAB is the tension in the string AB
TCD is the tension in the stnng CD
The eelatlon between tension and the wave speed is given by
$\text{v}=\sqrt{\frac{\text{T}}{\mu}}$
$\text{v}\propto\sqrt{\text{T}}$
where
v is the wave speed of the transverse wave
$\mu$ is the mass per unit length of the string
$\frac{\text{v}_1}{\text{v}_2}=\sqrt{\frac{\text{T}}{2\text{T}}}$
$=\frac{1}{\sqrt{2}}$
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