MHT CET · Physics · Waves and Sound
A pipe open at one end has length \(0.8 \mathrm{~m}\). At the open end of the tube a string \(0.5 \mathrm{~m}\) long is vibrating in its \(1^{\text {st }}\) overtone and resonates with fundamental frequency of pipe. If tension in the string is \(50 \mathrm{~N}\), the mass of string is (speed of sound \(=320 \mathrm{~m} / \mathrm{s}\) )
- A 25 gram
- B 15 gram
- C 20 gram
- D 10 gram
Answer & Solution
Correct Answer
(D) 10 gram
Step-by-step Solution
Detailed explanation
\(2 \times\left[\frac{1}{2 \ell_{1}} \sqrt{\frac{T}{m}}\right]=\frac{v}{4 \ell_{2}}\)
\(\frac{1}{0.5} \sqrt{\frac{50}{m}}=\frac{320}{4 \times 0.8}\)
\(\therefore \quad\) Total mass of the string \(=0.02 \times 0.5 \mathrm{~kg}=10 \mathrm{gm}\)
\(\therefore \quad 02 \mathrm{~kg} / \mathrm{m}\)
\(\frac{1}{0.5} \sqrt{\frac{50}{m}}=\frac{320}{4 \times 0.8}\)
\(\therefore \quad\) Total mass of the string \(=0.02 \times 0.5 \mathrm{~kg}=10 \mathrm{gm}\)
\(\therefore \quad 02 \mathrm{~kg} / \mathrm{m}\)
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