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BITSAT 2011
Exam
BITSAT
Year
2011
Subject
Physics
Chapter
Waves and Sound

BITSAT 2011 · Physics · Waves and Sound

The fundamental frequency of an open organ pipe is 300 Hz . The...

The fundamental frequency of an open organ pipe is 300Hz300 \mathrm{ Hz}. The first overtone of this pipe has same frequency as first overtone of a closed organ pipe. If speed of sound is 330m/s330 \mathrm{ m} / \mathrm{s}, then the length of closed organ pipe is

Options

  1. A41cm41 \mathrm{ cm}
  2. B37cm37 \mathrm{ cm}
  3. C31cm31 \mathrm{ cm}
  4. D80cm80 \mathrm{ cm}

Correct answer

A. 41cm41 \mathrm{ cm}

Step-by-step solution

For open pipe, n=v2ℓ,\mathrm{n}=\frac{\mathrm{v}}{2 \ell}, where n0\mathrm{n}_{0} is the fundamental frequency of open pipe. ∴ℓ=v2n=3302×300=1120\therefore \ell=\frac{\mathrm{v}}{2 \mathrm{n}}=\frac{330}{2 \times 300}=\frac{11}{20} As freq. of 1 st overtone of open pipe = freq. of 1 st overtone of closed pipe ∴2v2ℓ=3v4ℓ′⇒ℓ′=3ℓ4=34×1120=41.25cm\begin{aligned} \therefore \quad 2 \frac{\mathrm{v}}{2 \ell}=3 \frac{\mathrm{v}}{4 \ell^{\prime}} \Rightarrow \ell^{\prime} &=\frac{3 \ell}{4}=\frac{3}{4} \times \frac{11}{20} \\ &=41.25 \mathrm{ cm} \end{aligned}
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