Chapter 15, Problem 76A

To determine

To calculate: If the pitch of a closed pipe will increase or decrease when the temperature of the air rises.

Answer to Problem 76A

The pitch will increase if temperature is increased.

Explanation of Solution

Given:

The speed of sound increases with temperature.

The length of the pipe does not change.

Formula used:

The frequency of a closed pipe is given by the formula:

$f=\frac{v}{4L}$

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

Calculation:

In the equation, $f=v/4L$ , if length remains constant,

$f\propto v$

Frequency and velocity will be directly proportional. If velocity increases(with increasing temperature), the frequency will also increase. Since frequency is referred to as pitch, with increasing temperature, the pitch will also increase.

Conclusion:

The pitch will increase.