Two strings of copper are stretched to the same tension. If their cross-sectional areas are in the ratio $1…

Two strings of copper are stretched to the same tension. If their cross-sectional areas are in the ratio $1 : 4$, then the respective wave velocities will be in the ratio
  1. (a) $4 : 1$
  2. (b) $2 : 1$
  3. (c) $1 : 2$
  4. (d) $1 : 4$

Solution

$v = \sqrt{\frac{T}{\mu}} = \sqrt{\frac{T}{\rho s}}$ or $v \propto \frac{1}{\sqrt{s}}$ $\therefore \frac{v_1}{v_2} = \sqrt{\frac{s_2}{s_1}} = \sqrt{\frac{4}{1}} \Rightarrow \frac{v_1}{v_2} = \frac{2}{1}$

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