TS EAMCET · Physics · Waves and Sound
The speed of a transverse wave on a string is \(160 \mathrm{~m} / \mathrm{s}\). If the three resonant frequencies of this string respectively are \(160 \mathrm{~Hz}, 240 \mathrm{~Hz}\) and \(400 \mathrm{~Hz}\), the length of the string is
- A \(80 \mathrm{~cm}\)
- B \(100 \mathrm{~cm}\)
- C \(160 \mathrm{~cm}\)
- D \(200 \mathrm{~cm}\)
Answer & Solution
Correct Answer
(B) \(100 \mathrm{~cm}\)
Step-by-step Solution
Detailed explanation
Resonant frequencies are 160,240 and \(400 \mathrm{~Hz}\), so their simplest ratios are 160:240:400. i.e. \[ 2: 3: 5 \] Hence, 160 is second harmonic \[ \Rightarrow \quad 160=\frac{n v}{2} \text {, where } n=2 \] Substituting \(n=2\) and \(v=160 \mathrm{~ms}^{-1}\), we get…
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