TS EAMCET · Physics · Waves and Sound
The fundamental frequency of transverse wave of a stretched string subjected to a tension \(\mathrm{T}_1\) is 300 Hz. If the length of the string is doubled and subjected to a tension of \(\mathrm{T}_2\), the fundamental frequency of the transverse wave in the string becomes 100 Hz, then \(\mathrm{T}_2: \mathrm{T}_1=\)
(Linear density of the string is constant)
- A \(1: 2\)
- B \(3: 4\)
- C \(2: 3\)
- D \(4: 9\)
Answer & Solution
Correct Answer
(D) \(4: 9\)
Step-by-step Solution
Detailed explanation
\(f_1 = \frac{1}{2L_1}\sqrt{\frac{T_1}{\mu}}\) \(f_2 = \frac{1}{2(2L_1)}\sqrt{\frac{T_2}{\mu}} = \frac{1}{4L_1}\sqrt{\frac{T_2}{\mu}}\) \(\frac{f_1}{f_2} = \frac{\frac{1}{2L_1}\sqrt{\frac{T_1}{\mu}}}{\frac{1}{4L_1}\sqrt{\frac{T_2}{\mu}}} = 2\sqrt{\frac{T_1}{T_2}}\)…
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