# Ask a Physicist Answers

## How does temperature affect the sound of a flute? — S

The sound of a flute originates in the column of air inside it. As the flautist blows across the hole in the flute’s mouthpiece, the air column begins to vibrate in and out of the flute’s two main openings: the hole in its mouthpiece and the open end of its pipe. The pattern of open holes along the length of the flute complicates this vibration, but the basic idea remains the same: a column of trapped air is vibrating between two openings.

The nature of this vibration is fairly simple. The trapped air is elastic or “bouncy,” so that it opposes compressions or rarefactions in much the same way as a spring does. The vibrations that take place in this air involve air rushing toward the center of the flute pipe from both ends and then rush away from that center. This air motion repeats rhythmically, propelled by the air’s elastic nature. As air rushes toward the center of the pipe, the air there becomes denser and its pressure rises above atmospheric. That elevated pressure slows the inrushing air and soon turns it around. As air rushes away from the center of the pipe, the air there becomes less dense and its pressure drops below atmospheric. Once again the airflow slows and then turns around. This repetitive bouncing continues as long as the flautist’s breath keeps supplying the air column with energy.

The frequency of the vibration and the pitch the flute emits depend on the stiffness of the air and on its inertia. By stiffness, I mean how strongly the air column resists the inflow or outflow of air. By inertia, I mean how hard it is to change the speed and direction of the air’s motion. Stiffening the air column speeds up the vibration and raises both its frequency and its pitch. Increasing the air column’s inertia slows the vibration and lowers its pitch.

A short air column is naturally stiffer than a long one because the short column experiences a larger change in density and pressure for a given amount of added air. That’s why a shorter flute (one with more open holes or one that is replaced by a half-sized piccolo) emits higher pitched notes. And an air column that has less total mass (the measure of inertia) also emits higher pitched notes. Anything that reduces the mass of the air column without changing its stiffness will raise the flute’s pitch.

One way to lower the air column’s mass is to replace the air with helium. Since helium has such a low density, a flute full of helium will have a much higher pitch than one full of air. But there is a simpler way to decrease the air column’s mass: heat the air up. At atmospheric pressure, hot air is less dense than cold air. That’s because it takes fewer hot-air molecules to maintain atmospheric pressure than it does cold-air molecules. And with fewer air molecules in the flute, its air column has less mass and vibrates faster. Its pitch is higher.

One way to lower the air column’s mass is to replace the air with helium. Since helium has such a low density, a flute full of helium will have a much higher pitch than one full of air. But there is a simpler way to decrease the air column’s mass: heat the air up. At atmospheric pressure, hot air is less dense than cold air. That’s because it takes fewer hot-air molecules to maintain atmospheric pressure than it does cold-air molecules. And with fewer air molecules in the flute, its air column has less mass and vibrates faster. Its pitch is higher.

As a flute warms up during play, its pitch gradually rises and the flautist must lengthen it to keep its pitch steady. The mouthpiece slides along the main pipe and allows the overall pitch of the flute to change. Maintaining a steady temperature in a flute is part of the task of a skilled flautist, since changes in that temperature will shift the flute’s pitch and take it in or out of tune with the rest of the orchestra.

Answered by Lou A. Bloomfield of the University of Virginia.