TS EAMCET · Physics · Waves and Sound
Two uniform stretched strings \(A\) and \(B\), made of steel, are vibrating under the same tension. If the first overtone of \(A\) is equal to the second overtone of \(B\) and if the radius of \(A\) is twice that of \(B\), the ratio of the lengths of the strings is
- A 2 : 3
- B 1 : 2
- C 1 : 3
- D 1 : 4
Answer & Solution
Correct Answer
(C) 1 : 3
Step-by-step Solution
Detailed explanation
Given, 1st overtone of \(A=2\) nd overtone of \(B\) \(\begin{aligned} \Rightarrow & \frac{1}{l_1} \sqrt{\frac{T}{\pi r_1^2 d}} =\frac{3}{2 l_2} \sqrt{\frac{T}{\pi r_2^2 d}} \\ \Rightarrow & \frac{r_2}{r_1} =\frac{3}{2}\left(\frac{l_1}{l_2}\right) \end{aligned}\) But…
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