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21.5 noted about the flute, the fact that the holes are on the side makes very lit- 1;j'fP:TteJ1ice. The first open hole becomes an antinode because the air is free to in and out of the opening. 'j>"FlCo. .;'Jl\./.''''5 to Equations 21.17 and 21.18, a wind instrument's frequency on the speed of sound inside the instrument. But the speed of sound depends on the temperature of the air. When a wind player first blows into the iristrument, the air inside starts to rise in temperature. This increases the sound speed, which in turn raises the instrument's frequency for each note until the air iemperature reaches a steady state. Consequently, wind players must "warm up" before tuning their instrument. For strings, the speed appearing in Equation 21.17 is the wave speed on the string as determined by the tension, not the sound speed in air. Many wind instruments have a "buzzer" at one end of the tube, such as a vibrating reed on a saxophone or clarinet or vibrating lips on a trumpet or trom- bone. Buzzers like these generate a continuous range of frequencies rather than single notes, which is why they sound like a "squawk" if you play on just the mouthpiece without the rest of the instrument. When connected to the body of the instrument, most ofthose frequencies cause no response of the air molecules. But the frequency from the buzzer that matches the fundamental frequency of the instrument causes the build-up of a large-amplitude response at just that fre· quency-a standing-wave resonance. This is the energy input that generates and sustains the musical note. EXAMPLE 21.7 The notes on a clarinet A clarinet is 66 cm long. The speed of sound in warm air is 350 mls. What are the frequencies of the lowest note on a claro inet and of the next highest harmonic? MODEL A clarinet is an open-closed tube because the player's lips and the reed seal the tube at the upper end. SOLVE The lowest frequency is the fundamental frequency. For an open-closed tube, the fundamental frequency is v 350 mls 4L 4(0.66 m) = 133 Hz An open-closed tube has only odd harmonics. The next highest harmonic is m = 3, with frequency /3 = 3/J = 399 Hz. Except in unusual situations, a vibrating string plays only the musical note cor- responding to the fundamental frequency fi. Thus stringed instruments must use several strings in order to obtain a reasonable range of notes. By contrast, wind instruments can sound at the second or third harmonic of the tube of air (12 or 13)' These higher frequencies are sounded by overblowing (flutes, brass instruments) or with special register keys that open small holes in the side of the instrument to encourage the formation of an antinode at that point (clarinets, saxophones). The controlled use of these higher harmonics gives wind instruments a wide range of notes. 21.5

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