The production of sound during speech or singing is a complicated process. Let's concentrate on the mouth. A typical depth for t

Question

3 years ago

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The production of sound during speech or singing is a complicated process. Let's concentrate on the mouth. A typical depth for t

he human mouth is about 7.80cm , 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?

?1,?2,?3,?4 = __ cm

B) What are the frequencies of the first four harmonics you can produce if your mouth is open? Use 350m/s.

f1,f2,f3,f4 = __ Hz

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

?1,?2,?3,?4 = __ cm

D) What are the frequencies of the first four harmonics you can produce if your mouth is closed? Use 350m/s.

f1,f2,f3,f4 = __ Hz

Physics

1 answer:

Pani-rosa [81] · Answer 1 · 2022-03-17T08:12:40+03:00

Answer:

a) λ₁ = 15.6 cm, λ₂ = 7.8 cm, λ₃ = 5.2 cm, λ₄ = 3.9 cm

b) f₁ = 2243 Hz, f₂ = 4487 Hz, f₃ = 6730 Hz, f₄ = 8974 Hz

c) λ₁ = 31.2 cm , λ₂ = 10.4 cm, λ₃= 6.24 cm, λ₄= 4.46 cm

d) f₁ = 1121.8 Hz , f₂ = 3365 Hz , f₃ = 5609 Hz , f₄ = 7848 Hz

Explanation:

a) This simulation can be approximated as a tube that is open at both ends, in this case we have wave maximums at these points, the relationship between the wavelength and the length of the wave is

λ = 2L

λ₂ = (2L) / 2

λ₃ = (2L) / 3

λₙ = 2L / n

n = 1, 2, 3 ...

Let's apply this equation to our case

λ = 2 7.80 cm

λ₁ = 15.6 cm

λ₂ = 2 7.8 / 2

λ₂ = 7.8 cm

λ₃ = 2 * 7.8 / 3

λ₃ = 5.2 cm