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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
\[\sqrt{2}\]
\[1/\sqrt{2}\]
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Solution
\[1/\sqrt{2}\]
\[T_{AB} = T\]
\[ T_{CD} = 2T\]
where
TAB is the tension in the string AB
TCD 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
\[\frac{v_1}{v_2} = \sqrt{\frac{T}{2T}} = \frac{1}{\sqrt{2}}\]
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