TS EAMCET · Physics · Waves and Sound
A sonometer wire has a length of \(114 \mathrm{~cm}\), between two fixed ends. Where should two bridges be placed so as to divide the wire into three segments (in \(\mathrm{cm}\) ) whose fundamental frequencies are in the ratio \(1: 3: 4\) ?
- A \(l_1, l_2, l_3=18,24,72\)
- B \(l_1, l_2, l_3=24,18,72\)
- C \(l_1, l_2, l_3=72,18,24\)
- D \(l_1, l_2, l_3=72,24,18\)
Answer & Solution
Correct Answer
(D) \(l_1, l_2, l_3=72,24,18\)
Step-by-step Solution
Detailed explanation
If length of the wire between the two bridges is \(l\), the frequency of vibration \(n=\frac{1}{2 l} \sqrt{\frac{T}{m}}\) \(\therefore \quad n \propto \frac{1}{l}\) Therefore, \(n_1: n_2: n_3=\frac{1}{l_1}: \frac{1}{l_2}: \frac{1}{l_3}\)…
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