A closed pipe is suddenly opened and changed to an open pipe of same length. The fundamental frequency of the resulting open pipe is less than that of $3^{r d}$ harmonic of the earlier closed pipe by $55 H z$ . Then, the value of fundamental frequency of the closed pipe is:

165 H z

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110 H z

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55 H z

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220 H z

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Solution

The correct option is A $55 H z$
Let the length of the pipe be $L$ and speed of sound in air be $v$
Fundamental frequency of open pipe $ν_{1} = \frac{v}{2 L}$
Frequency of $3 r d$ harmonic in closed pipe $ν_{3}^{'} = \frac{3 v}{4 L}$

According to the question, $ν_{3}^{'} - ν_{1} = 55$
$∴$ $\frac{3 v}{4 L} - \frac{v}{2 L} = 55$ $⟹ \frac{v}{4 L} = 55$
So, fundamental frequency of closed pipe: $ν_{1}^{'} = \frac{v}{4 L} = 55 H z$

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A closed pipe is suddenly opened and changed to an open pipe of same length. The fundamental frequency of the resulting open pipe is less than that of 3rd harmonic of the earlier closed pipe by 55 Hz. Then, the value of fundamental frequency of the closed pipe is:

A closed pipe is suddenly opened and changed to an open pipe of same length. The fundamental frequency of the resulting open pipe is less than that of $3^{r d}$ harmonic of the earlier closed pipe by $55 H z$ . Then, the value of fundamental frequency of the closed pipe is: