Review. An aluminum pipe is open at both ends and used as a...

Review. An aluminum pipe is open at both ends and used as a flute. The pipe is cooled to $5.00^{\circ} \mathrm{C},$ at which its length is 0.655 $\mathrm{m}$ . As soon as you start to play it, the pipe fills with air at $20.0^{\circ} \mathrm{C}$ . After that, by how much does its fundamental frequency change as the metal rises in temperature to $20.0^{\circ} \mathrm{C} ?$

Key Concepts

Temperature Dependence of the Speed of Sound

The speed of sound in a gas varies with temperature because warmer air has particles that move faster, allowing sound waves to propagate more quickly. In many practical applications, including musical instruments like flutes, the sound speed is a function of the temperature of the air filling the instrument. Although the air temperature may be held constant while the instrument itself warms up, understanding this concept helps differentiate between changes in sound propagation properties and changes in the physical dimensions of the instrument.

Acoustic Resonance in Open Pipes

Acoustic resonance in open pipes is a phenomenon where sound waves form standing wave patterns within a tube that is open at both ends. The fundamental frequency of an open pipe is determined by the relationship f = v/(2L), where v is the speed of sound in the medium and L is the length of the pipe. Changing the length of the pipe, for instance due to thermal expansion, directly affects the frequency produced, making it a critical concept in the design and tuning of wind instruments.

Thermal Expansion

Thermal expansion refers to the tendency of materials to change in size or shape with temperature. As the temperature increases, most solids expand due to the increased vibration of atoms within the material. This concept is important because even small changes in dimensions, such as the length of a pipe, can affect physical properties or performance in applications like musical instruments, where dimensions directly influence resonant frequencies.

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