TS EAMCET · Physics · Waves and Sound
A string vibrates in its fundamental mode when a tension \(T_1\) is applied to it. If the length of the string is decreased by \(25 \%\) and the tension applied is changed to \(\mathrm{T}_2\), the fundamental frequency of the string increases by \(100 \%\), then \(\frac{\mathrm{T}_2}{\mathrm{~T}_1}=\) (Linear density of the string is constant)
- A \(\frac{3}{8}\)
- B \(\frac{2}{3}\)
- C \(\frac{8}{9}\)
- D \(\frac{9}{4}\)
Answer & Solution
Correct Answer
(D) \(\frac{9}{4}\)
Step-by-step Solution
Detailed explanation
\(f_1 = \frac{1}{2L_1} \sqrt{\frac{T_1}{\mu}}\) \(L_2 = L_1 - 0.25L_1 = 0.75L_1 = \frac{3}{4}L_1\) \(f_2 = f_1 + 100\% f_1 = 2f_1\) \(f_2 = \frac{1}{2L_2} \sqrt{\frac{T_2}{\mu}}\)…
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