Question

Both the strings, shown in figure (15-Q1), 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 ${\nu }_1/{\nu }_2$ is
(a) 1
(b) 2
(c) $\sqrt{2}$
(d) $1/\sqrt{2}$.

Answer 1

(d) $1/\sqrt{2}$


$$\begin{gathered} T_{\mathrm{AB}}=T \\ {T}_{\mathrm{CD}}=2T \end{gathered}$$
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
$$\begin{gathered} v=\sqrt{\frac{T}{\mathit{\mu }}} \\ v\propto \sqrt{T} \end{gathered}$$
where
v is the wave speed of the transverse wave
μ is the mass per unit length of the string
$\frac{v_1}{v_2}=\sqrt{\frac{T}{2T}}=\frac{1}{\sqrt{2}}$