Question

The first and second formants when you make an "ee" vowel sound are approximately 270 Hz and 2300 Hz. The speed of sound in your vocal tract is approximately 350 m/s. If you breathe a mix of oxygen and helium (as deep-sea divers often do), the speed increases to 810 m/s .

Answer 1

λ₂ = 3 m , λ₃ = 0.352 m

Step-by-step explanation:

To find the new wavelengths we use the relationship between the speed of sound and the wavelength and frequency

v = λ f

The frequency of vibration for being a resonant process does not change from one medium to another, therefore the frequency must change

For the first frequency

f₀ = 270 Hz λ = 350/270 = 1.30 m

λ₂ = v₂ / f₀

λ₂ = 810/270

λ₂ = 3 m

f₀ = 2300 Hz λ = 350/2300 = 0.152 m

λ₃ = 810/2300

λ₃ = 0.352 m

We can see that the wavelength is significantly lengthened when helium is breathed