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JIPMER 2010
Exam
JIPMER
Year
2010
Subject
Physics
Chapter
Waves and Sound

JIPMER 2010 · Physics · Waves and Sound

Two vibrating strings of the same material but lengths L and 2 L...

Two vibrating strings of the same material but lengths LL and 2L2 L have radii 2r2 r and rr respectively. They are stretched under the same tension. Both the strings vibrate in their fundamental modes, the one of length LL with frequency v1v_1 and the other with frequency v2v_2. The ratio v1/v2v_1 / v_2 is

Options

  1. A2
  2. B4
  3. C8
  4. D1

Correct answer

D. 1

Step-by-step solution

Fundamental frequency, v=12lTm=12lTπr2ρ or v∝1lr∴v1v2=l2r2l1r1=2L×rL×2r=1\begin{array}{ll} & v=\frac{1}{2 l} \sqrt{\frac{T}{m}}=\frac{1}{2 l} \sqrt{\frac{T}{\pi r^2 \rho}} \\ \text{ or } & v \propto \frac{1}{l r} \\ \therefore & \frac{v_1}{v_2}=\frac{l_2 r_2}{l_1 r_1}=\frac{2 L \times r}{L \times 2 r}=1 \end{array}
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