Final answer:
The effective length is calculated to be approximately 0.142 meters or 14.23 centimeters. To find the effective length of the vocal tract for a fundamental tone of 620 Hz, we use the formula for the fundamental frequency of a closed pipe and account for the speed of sound in air at body temperature.
Step-by-step explanation:
To find the effective length of the vocal tract in a person whose fundamental tone is 620 Hz when treated as a pipe closed at one end, we need to use the formula for the fundamental frequency of such a pipe, which is:
f = v / (4L)
Here, f is the fundamental frequency, v is the speed of sound in air at the temperature of the body, and L is the length of the pipe.
Assuming body temperature to be 37.0°C, the speed of sound in air, v, can be calculated using the fact that the speed of sound increases with temperature.
The speed of sound at 0°C is approximately 331 m/s and increases by 0.6 m/s for each degree Celsius increase in temperature.
To find the speed of sound at body temperature, we use:
v = 331 m/s + (0.6 m/s/°C) × (37.0°C)
v = 331 m/s + 22.2 m/s
= 353.2 m/s
Now we can solve for L as follows:
L = v / (4f)
L = 353.2 m/s / (4 × 620 Hz)
L = 353.2 m/s / 2480 Hz
L = 0.1423 m
So the effective length of the vocal tract is approximately 0.142 meters or 14.23 centimeters.