Chapter 15, Problem 78A

To determine

To calculate: If the pitch of a sound increases or decreases if a closed pipe is changed into an open pipe.

Answer to Problem 78A

The pitch is increased if the closed pipe is made an open pipe.

Explanation of Solution

Given:

A closed pipe is changed into an open pipe.

Formula used:

Frequency of a closed pipe is given by the formula:

$f=v/4L$

Where $v$ is velocity and $L$ is length.

Frequency of an open pipe is given by the formula:

$f=v/2L$

Where $v$ is velocity and $L$ is length.

Calculation:

Let frequency of the closed pipe be $fa$ and that of the open pipe be $fb$ . The frequency of the closed pipe can be calculated as:

$\begin{array}{l}fa=\frac{v}{4L}\\ fa=\frac{1}{2}\cdot \frac{v}{2L}\\ fa=\frac{1}{2}fb\\ fb=2fa\end{array}$

The frequency of the open pipe( $fb$ ) will be twice that of the closed pipe( $fa$ ).

Conclusion:

The pitch is increased if the closed pipe is made an open pipe.