When open pipe is closed from one end then third overtone of closed pipe is higher in frequency by $150…

When open pipe is closed from one end then third overtone of closed pipe is higher in frequency by $150 \mathrm{~Hz}$ than second overtone of open pipe. The fundamental frequency of open end pipe will be
  1. 300Hz
  2. 500Hz
  3. 200Hz
  4. 400Hz

Solution

$3^{\mathrm{rd}}$ overtone of closed pipe $=7 \mathrm{n}_{\mathrm{oc}}=\frac{7 \mathrm{v}}{4 \ell}$ $2^{\text {nd }}$ overtone of closed pipe $=3 \mathrm{n}_{oc}=\frac{3 \mathrm{v}}{2 \ell}$ Now, $\frac{7 \mathrm{v}}{4 \ell}=\frac{3 \mathrm{v}}{2 \ell}+150$ $\frac{7 v}{4 \ell}-\frac{3 v}{2 \ell}=150$ $\frac{7 v-6 v}{4 \ell}=150$ $\frac{v}{4 \ell}=150$ $\begin{array}{ll}\therefore \quad \ell= & \frac{v}{4 \times 150} \\ \therefore \quad & n_{oc}=\frac{v}{2 \ell}=\frac{v \times 4 \times 150}{2 \times v}=300 \mathrm{~Hz}\end{array}$

Asked in: MHT CET 2020 (16 Oct Shift 1)

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