Question

Deep-sea divers often breathe a mixture of helium and oxygen to avoid getting the "bends" from breathing high-pressure nitrogen. The helium has the side effect of making the divers' voices sound odd. Although your vocal tract can be roughly described as an open-closed tube, the way you hold your mouth and position your lips greatly affects the standing-wave frequencies of the vocal tract. This is what allows different vowels to sound different. The "ee" sound is made by shaping your vocal tract to have standing-wave frequencies at, normally, 270 Hz and 2300 Hz.What will these frequencies be for a helium-oxygen mixture in which the speed of sound at body temperature is 750 m/s? The speed of sound in air at body temperature is 350 m/s.

Answer 1

Answer:

0.69444 m, 0.08152 m, 0.32407 m, 0.03804 m

Explanation:

v = Velocity of sound

f = Frequency

Length of vocal tract is given by

$L=\dfrac{v}{4f}$

At f = 270 Hz v = 750 m/s

$L=\dfrac{750}{4\times 270}\\\Rightarrow L=0.69444\ m$

At f = 2300 Hz v = 750 m/s

$L=\dfrac{750}{4\times 2300}\\\Rightarrow L=0.08152\ m$

At f = 270 Hz v = 350 m/s

$L=\dfrac{350}{4\times 270}\\\Rightarrow L=0.32407\ m$

At f = 2300 Hz v = 350 m/s

$L=\dfrac{350}{4\times 2300}\\\Rightarrow L=0.03804\ m$