Question

Both the strings, shown in figure, are made of same material and have same cross section. The pulleys are light. The wave speed of a transverse wave in the string AB is
\[\nu_1\]  and in CD it is \[\nu_2\]. Then \[\nu_1 / \nu_2\]

Options

• 1

• 2

• \[\sqrt{2}\]

• \[1/\sqrt{2}\]

Answer 1

\[1/\sqrt{2}\]

\[T_{AB}  = T\] 

\[ T_{CD}  = 2T\]

where
          ​T_AB is the tension in the string AB
          ​T_CD is the tension in the string CD
The eelation between tension and the wave speed is given by

\[v = \sqrt{\frac{T}{\mathrm{\mu}}}\] 

\[v \propto \sqrt{T}\]
where
          v is the wave speed of the transverse wave
           μ is the mass per unit length of the string
\[\frac{v_1}{v_2} = \sqrt{\frac{T}{2T}} = \frac{1}{\sqrt{2}}\]