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Waves question

2023 · Q143
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Waves question

2023 · Q143

NEETPhysicsWavesMCQ+4 / −1

The 4th 4^{\text {th }}4th  overtone of a closed organ pipe is same as that of 3rd 3^{\text {rd }}3rd  overtone of an open pipe. The ratio of the length of the closed pipe to the length of the open pipe is :

  1. A
    8 : 9
  2. B
    9 : 7
  3. C
    9 : 8
  4. D
    7 : 9
View written solutionFree

Correct answer: C

$$\begin{aligned} & \mathrm{n}_{\text {oop }}=(2 \mathrm{M}+1)^{\text {th }} \text { Har. }=(2 \times 4+1) \times \frac{\mathrm{V}}{4 \ell_{\mathrm{c}}}=\frac{9 \mathrm{~V}}{4 \ell_{\mathrm{c}}} \\ & \mathrm{n}_{\text {oop }}=(\mathrm{M}+1)^{\text {th }} \text { Har. }=(3+1) \frac{\mathrm{V}}{2 \ell_0}=\frac{4 \mathrm{~V}}{2 \ell_0} \\ & \text { now } \frac{9 \mathrm{~V}}{4 \ell_{\mathrm{c}}}=\frac{4 \mathrm{~V}}{2 \ell_0} \\ & \frac{\ell_{\mathrm{c}}}{\ell_0}=\frac{18}{16}=\frac{9}{8} \end{aligned} $$

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