Understanding Fundamental Frequency in Voice Production

What is the fundamental frequency (in Hz) if the resonating tube is 0.210 m long at an air temperature of 37.0°C?

a) 408.33 Hz

What would be the frequency (in Hz) if the air was replaced with helium at the same temperature?

b) 1199.4 Hz

Answer:

The fundamental frequency of voice production can be approximated by considering the breathing passages and mouth as a resonating tube closed at one end.

To find the fundamental frequency, we use the formula:

f = v / (4L)

Where f is the fundamental frequency, v is the speed of sound in air, and L is the length of the tube.

At an air temperature of 37.0°C, the speed of sound in air is approximately 343 m/s.

Plugging in the values, we get:

f = 343 / (4 * 0.210)

f ≈ 408.33 Hz

Therefore, the fundamental frequency of the voice production is approximately 408.33 Hz.

If the air is replaced with helium, the speed of sound in helium is higher. At the same temperature, the speed of sound in helium is approximately 1007 m/s.

Using the same formula:

f = 1007 / (4 * 0.210)

f ≈ 1199.4 Hz

Therefore, if the air is replaced with helium, the fundamental frequency would be approximately 1199.4 Hz.