Question

How will the air temperature in a room affect the pitch of organ pipes?

Short answer

When the temperature in the room changes, the frequency of sound in the organ pipe changes. The speed of sound will increase with the increase in temperature, and hence the pitch of the sound in the pipe will also increase.

Step-by-step solution

Effect of temperature on sound wave

The following equation gives the relationship between the velocity of sound and temperature:

\(v = \left( {331 + 0.60T} \right)\;{{\rm{m}} \mathord{\left/{\vphantom {{\rm{m}} {\rm{s}}}} \right.} {\rm{s}}}\)

The equations give the pitch for a closed organ pipe and open organ pipe:

\({f_{{\rm{closed}}}} = \frac{{nv}}{{4l}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {n\;{\rm{odd integer}}} \right)\)

\({f_{{\rm{open}}}} = \frac{{nv}}{{2l}}\)

In both the mentioned case, the frequency is proportional to the velocity of the sound wave. The speed is a function of temperature, and the frequency is also a function of temperature.

Relationship between the speed of the sound wave, temperature, and frequency

In each case, when the speed of the sound wave increases, the frequency of the wave alos increases, or the frequency is directly related to the speed of sound in air.

Since the speed is a function of temperature, the length is fixed, the frequency is also a function of temperature.

As the speed of sound increases with temperature, the pitch of the pipe also increases with the temperature.