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 8.00 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. A) What are the wavelengths of the first four harmonics you can produce if your mouth is open? (in cm/4 answers) B)What are the frequencies of the first four harmonics you can produce if your mouth is open? Use 354 (in Hz/4 answers) C)What are the wavelengths of the first four harmonics you can produce if your mouth is closed? (in cm/4 answers) D)What are the frequencies of the first four harmonics you can produce if your mouth is closed?

Answer 1

Answer:A) The wavelengths are:8cm for first harmonic

5.3cm for second harmonic

4cm for third harmonic

3.2cm for fourth harmonic

B) The frequencies are:

44.25Hz for first harmonic

66.38Hz for second harmonic

88.5Hz for third harmonic

110.63Hz for fourth harmonic

C) The wavelengths are:

10.66Cm for first harmonic

6.4 cm for second harmonic

4.57cm for third harmonic

3.5cm for fourth harmonic

D) The frequencies are:

33.19Hz for first harmonic

55.31 Hz for second harmonic

77.44Hz for third harmonic

99.56Hz for fourth harmonic

Explanation: since the mouth is being modelled as an organ pipe, then we can say that an open mouth is a model of an organ pipe open at both ends.

For an open pipe all harmonics are possible but only odd harmonic's are possible in closed pipes. A closed mouth is a model of a closed pipe, since closed pipes are open at one end.