Q123 / 150 · MHT CET 2020 (16 Oct Shift 2) · Physics

An open organ pipe and a closed organ pipe have the frequency of their first overtone identical. The ratio of length of open pipe to that of closed pipe is

  • A
    3:4
  • B
    1:2
  • C
    2:1
  • Correct answer
    D
    4:3

Solution

(D) $\frac{\ell_{0}}{\ell_{c}}=?$ $\begin{array}{ll}\text { For closed pipe } & n_{p}=n_{0}(2 p+1) \Rightarrow n_{l c}=n_{o}^{3} \\ \text { For open pipe } & n_{p}=n_{0}(p+1) \Rightarrow n_{l o}=n_{0}^{2}\end{array}$ $\begin{aligned} & n_{1 c}=3 n_{0}=\frac{3 V}{4 \ell_{c}} \\ & n_{10}=2 n_{0}=\frac{2 V}{2 \ell_{0}} \\ \therefore & \frac{3 V}{4 \ell_{c}}=\frac{2 V}{2 \ell_{0}} \\ \therefore & \frac{\ell_{0}}{\ell_{c}}=\frac{4}{3} \end{aligned}$

Hence, the correct answer is option: 'D'.

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