The production of sound during speech or singing is a complicated process. Let\'

Question

The production of sound during speech or singing is a complicated process. Let's concentrate on the mouth. A typical depth for the human mouth is about 7.50 cm , although this number can vary. (Check it against your own mouth.). We can model the mouth as an organ pipe that is open at the back of the throat.

1)What are the wavelengths of the first four harmonics you can produce if your mouth is open?

2)What are the frequencies of the first four harmonics you can produce if your mouth is open? Use 354 m/s.

3)What are the wavelengths of the first four harmonics you can produce if your mouth is closed?

4)What are the frequencies of the first four harmonics you can produce if your mouth is closed? Use 354 m/s.

Explanation / Answer

(1)

since organ pipe is open closed pipe, the wave lenght present in the pipe is

1= 4L = 4x0.075 =0.3m

2= 4L/3 = 4x0.075/3 =0.1m

3= 4L/5 = 4x0.075/5 =0.06m

3= 4L/7 = 4x0.075/7 =0.042m

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(2)

f1 = v/ 1 = 354/0.3 = 1180 Hz

f2 = v/ 2 = 354/0.1 = 3540 Hz

f3 = v/ 3 = 354/0.06 = 5900 Hz

f4 = v/ 4= 354/0.042 = 8428.57 Hz

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(3)

1= 2L = 2x0.075 =0.15m

2= L = 0.075 m

3= 2L/3 = 2x0.075/3 =0.05m

4= L/2 = 0.075/2 =0.0375m

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f1 = v/ 1 = 354/0.15 = 2360 Hz

f2 = v/ 2 = 354/0.075 =4720 Hz

f3 = v/ 3 = 354/0.05 = 7080 Hz

f4 = v/ 4= 354/0.0375 = 9440 Hz

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