Divers working in underwater chambers at great depths must

Chapter , Problem 57

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Divers working in underwater chambers at great depths must deal with the danger of nitrogen narcosis (the bends), in which nitrogen dissolves into the blood at toxic levels. One way to avoid this danger is for divers to breathe a mixture containing only helium and oxygen. Helium, however, has the eff ect of giving the voice a highpitched quality, like that of Donald Ducks voice. To see why this occurs, assume for simplicity that the voice is generated by the vocal cords vibrating above a gas-fi lled cylindrical tube that is open only at one end. The quality of the voice depends on the harmonic frequencies generated by the tube; larger frequencies lead to higher-pitched voices. Consider two such tubes at 20 8C. One is fi lled with air, in which the speed of sound is 343 m/s. The other is fi lled with helium, in which the speed of sound is 1.00 3 103 m/s. To see the eff ect of helium on voice quality, calculate the ratio of the nth natural frequency of the helium-fi lled tube to the nth natural frequency of the air-fi lled tube.

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