Question

The HumanVoice. The human vocal tract is a pipe that extendsabout 16 cm from the lips to thevocal folds (also called the "vocal cords") near the middle of yourthroat. The vocal folds behave rather like the reed of a clarinet,and the vocal tract acts like a stopped pipe. Estimate the firstthree standing-wave frequencies of the vocal tract.Use v = 344 m/s. (The answers are only anestimate, since the position of lips and tongue affects the motionof air in the vocal tract.)lowest frequencyHzsecond frequencyHzthird frequencyHz

Answer 1

Lowest frequency = 537.5 Hz

Third frequency=2687.5 Hz

Step-by-step explanation:

Given that

Length of pipe ,L= 16 cm

Speed of sound,V = 344 m/s

Also given that it behave like stopped pipe and we know that fundamental frequency for this type of system given as

`f_1=(V)/(4L)`

Now by putting the values

`f_1=(344)/(4* 0.16)`

`f_1=537.5 Hz`

Now second harmonic frequency

`f_2=3f_1`

`f_2=3* 537.5\ Hz`

`f_2=1612.5\ Hz`

Now third harmonic frequency

`f_3=5f_1`

`f_3=5* 537.5\ Hz`

`f_3=2687.5\ Hz`