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 7.10 , 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. -What are the wavelengths of the first four harmonics you can produce if your mouth is open? -What are the frequencies of the first four harmonics you can produce if your mouth is open? Use 349 -What are the wavelengths of the first four harmonics you can produce if your mouth is closed? -What are the frequencies of the first four harmonics you can produce if your mouth is closed? Use 349

Explanation / Answer

The frequencies for an organ pipe closed at one end are f = v /? In the first mode of vibration the open end is an anti node and the very next node is at the closed end. Hence L = ?1/4 ?1= 4L = 4x0.08 =0.32 m f1 = v /?1 = v / 4L = 354/4x0.08 = 1106 Hz In the second mode the length L consists of two nodes and an anti node at the open end. Hence L = (3/4)?2 ?2 = 4L/3 = 0.32/3 = 0.107 m f2 = v / ?2 =354/0.107 = 3308.4 Hz ?3 = 4L/5 = 0.064 m f3 = v / ?3 = 354/0.064 = 5531.25 Hz

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