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.

Short answer

The new range could be within $(579--4930)$Hz

Step-by-step solution

Relationship between wave and sound frequency 

Wavelength is proportional to the sound and its frequency. Higher frequencies have shorter wavelengths and vice versa.

Identification of the new frequency range  

Frequency is proportional to the sound speed. The increasing speed sound is from 350 to 750 and will increase up to $\frac{75}{35}$m/s.

the new range frequency will be$$\begin{gathered} f_{min}=270·\frac{75}{35}=\frac{579Hz}{} \\ {f}_{max}=2300·\frac{75}{35}=\frac{4930Hz}{} \end{gathered}$$