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MHT CET · Physics · Waves and Sound

A pipe closed at one end has length \(0.8 \mathrm{~m}\). At its open end \(0.5 \mathrm{~m}\) long uniform string is vibrating in its \(2^{\text {nd }}\) harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the wire is \(50 \mathrm{~N}\) and the speed of sound is \(320 \mathrm{~m} / \mathrm{s}\), the mass of the string is

  1. A 20 gram
  2. B 10 gram
  3. C 5 gram
  4. D 15 gram
Verified Solution

Answer & Solution

Correct Answer

(B) 10 gram

Step-by-step Solution

Detailed explanation

\(\begin{aligned} & 2 \times\left[\frac{1}{2 \ell_1} \sqrt{\frac{\mathrm{T}}{\mathrm{m}}}\right]=\frac{v}{4 \ell_2} \\ & \frac{1}{0.5} \sqrt{\frac{50}{\mathrm{~m}}}=\frac{320}{4 \times 0.8} \\ & \therefore \mathrm{m}=0.02 \mathrm{~kg} / \mathrm{m} \\ & \therefore \text { Total mass of the string } \\ & =0.02 \times 0.5 \mathrm{~kg}=10 \mathrm{gm}\end{aligned}\)