The coval tract can be assumed to act like a cylindrical tube closed at one end (at the larynx), having a length of 17.5 cm. On the basis of this, what would you expect to be the first three formant frequencies of the voice?
To determine the first three formant frequencies of the voice based on the assumptions that the vocal tract acts like a cylindrical tube closed at one end (at the larynx) with a length of 17.5 cm, we need to consider the resonant frequencies of this tube.
The resonant frequencies of a closed cylindrical tube, such as the vocal tract, can be approximated by the formula:
fn = (n * c) / (2L)
Where:
fn is the resonant frequency (formant frequency)
n is the order of the formant
c is the speed of sound in air
L is the length of the tube
Given that the length of the vocal tract is 17.5 cm, we can convert it to meters by dividing by 100:
L = 17.5 cm / 100 = 0.175 meters
The speed of sound in air is approximately 343 meters per second, but it can vary with temperature, humidity, and altitude.
Now, let's calculate the first three formant frequencies (f1, f2, and f3) using the formula with n = 1, 2, and 3:
f1 = (1 * c) / (2L)
f2 = (2 * c) / (2L)
f3 = (3 * c) / (2L)
You can substitute the values into the formulas to calculate the frequencies. However, since the speed of sound in air can vary, it's challenging to provide an exact answer without knowing the specific conditions (temperature, humidity, and altitude) at which this calculation is being performed.
To get the most accurate result, you can look up the speed of sound in air for the given conditions, substitute the values into the formulas, and calculate the first three formant frequencies accordingly.