The pan flute is a musical instrument consisting of a number...

The pan flute is a musical instrument consisting of a number of closed-end tubes of different lengths. When the musician blows over the open ends, each tube plays a different note. The longest pipe is $0.33 \mathrm{m}$ long. What is the frequency of the note it plays?

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Key Concepts

Standing Waves in Closed Pipes

In a closed-end tube, standing waves are formed when sound waves reflect off the boundaries. The closed end must always be a node (point of no displacement), and the open end becomes an antinode (point of maximum displacement). The lowest frequency mode (fundamental frequency) in such a setup has a wavelength that is four times the length of the tube.

Frequency Calculation of Sound Waves

The frequency of a sound wave is determined by the relationship f = v/?, where f is the frequency, v is the speed of sound, and ? is the wavelength. In the case of a closed-end pipe, the effective wavelength for the fundamental frequency is four times the length of the instrument, so the frequency can be calculated using f = v/(4L).

Speed of Sound in Air

The speed of sound in air, typically around 343 meters per second under ordinary conditions, is essential in connecting the physical dimensions of a musical instrument to the sound it produces. It represents how fast sound energy travels through the medium and is used to determine the frequency when combined with the wavelength.

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