Question

Divers working deep in the ocean breathe a mixture of gases, of which 97 % is helium [12]. the speed of sound in helium is 965 m/s. how does this affect the first two formants of the diver's voices? (hint: the formant frequency is proportional to the speed of sound in the gas that fills the cavity.)

Answer 1

The speed of sound in normal air is approximately $343~m/s$. In helium, instead, it is $965~m/s$. The mixture of gases mentioned in the problem is made of 97 % of helium and 3% of normal air, therefore the speed of sound in this mixture will be
$c= \frac{97}{100}965~m/s + \frac{3}{100} 343~m/s = 946~m/s$
So, the ratio between the speed of sound in this mixture of gases and in normal air is
$r= \frac{946~m/s}{343~m/s}=2.76$
The frequencies of the formants of the diver's voices are proportional to the speed of sound, therefore they will change by the same proportion as the speed of sound does. So, the frequencies will be 2.76 times higher than in normal air.