The human vocal tract is a pipe that extends about 17 cm from the lips to the vocal folds (a. k. a. vocal cords) near the middle of your throat. The vocal folds behave rather like the reed of a clarinet, and the vocal tract acts like a closed pipe. Estimate the first three standing wave frequencies of the vocal tract if the sound waves will travel at 344 m/s in the tract.

f₁ = 505.9 Hz, f₃ = 1517.6 Hz, f₅ = 2529.4 Hz

Explanation:

The production of standing waves is the sum of two waves of equal frequency that travel in the opposite direction, for a system with a closed side, another open is described by a node in the closed part and a belly (antinode) in the open part

λ₁ = 4L

λ₃ = 4L / 3

λ₅ = 4L / 5

The general relationship is

λ = 4L / n n = 1, 3, 5, 7 ...

Let's use the speed of the wave

v = λ f

f = v / λ

f = n v / 4L

Let's calculate the first frequencies

n = 1

f₁ = 1 344 / (4 0.17)

f₁ = 505.9 Hz

n = 3

f₃ = 3 344 / (4 0.17)

f₃ = 1517.6 Hz

n = 5

f₅ = 5 344 / (4 0.17)

f₅ = 2529.4 Hz