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 750 m/s. With this mix of gases, what are the frequencies of the two formants?

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zubairpu427 zubairpu427 · Answer 1 · 2020-02-10T07:51:06+01:00

Answer:

Answers are:

1. Frequency of first formant = 633 Hz

2. Frequency of second formant = 5403 Hz

Explanation:

Data available:

first formant frequency = f1 = 270 Hz

Second formant frequency = f2 = 2300 Hz

Speed of sound in vocal tract = 320 m/s

Speed of sound in vocal tract in deep sea = 750 m/s

Required:

First formant frequency = ?

Second Formant Frequency = ?

Solution :

We know that

FUndamental Frequency of standing wave mode tube L is

[tex]f1=v/4L[/tex]

We will solve it for L for both frequencies given

Length for first formant frequency

[tex]L=v/4f1=320/4*270=0.296[/tex]

Length for second formant frequency

[tex]L=v/4f2=320/4*2300=0.0347[/tex]

Now we will calculate the frequencies when a deep sea diver uses helium and oxygen mixture.

Frequency for first formants.

[tex]f1=v/4L=750/4*0.296=633.4 Hz[/tex]

Frequency for first formants.

[tex]f1=v/4L=750/4*0.0347= 5403Hz[/tex]