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 8.50 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.
~ What are the wavelengths of the first 4 harmonics you can produce in your mouth is open?

~ What are the frequencies of the first 4 harmonics you can produce if your mouth is open. Use 351 m/s.

~ What are the wavelengths of the first 4 harmonics you can produce if your mouth is closed?

~ What are the frequencies of the first 4 harmonics you can produce if your mouth is closed.   Use 351 m/s.

Answer 1

Given L = 8.5 cm

For open pipe

a) lambda = 2*L/n

n =1, lambda1 = 2 * 8.5 = 17 cm

n=2, lambda2 = 2*L/2 = L = 8.5 cm

n = 3, lambda3 = 2*L/3 = (2*8.5/3) = 5.66 cm

n=4, lambda4 = 2*L/4 = 8.5/2 = 4.25 cm

b)

fn = n*v/(2L)

n=1, f1 = 1*351/(2*0.085) , f1 = 2064.7 Hz

n=2, f2 = 2*f1 = 4129.4 Hz

n=3, f3 = 3*f1 = 6194.1 Hz

n=4, f4 = 4*f1 = 8258.8 Hz

For closed pipe

a)

lambda = 4*L/n   (n = 1,3,5,7------------)

n =1, lambda1 = 4 * 8.5 = 34 cm

n=2, lambda2 = 4*L/3 = L = 11.33 cm

n = 3, lambda3 = 4*L/5 = 6.8 cm

n=4, lambda4 = 4*L/7 = 4.85 cm

b)

fn = n*v/(4L)    ( n = 1,3,5,7-----------)

n=1, f1 = 1*351/(4*0.085) , f1 = 1032.35 Hz

n=3, f2 = 3*f1 = 3097.05 Hz

n=5, f3 = 5*f1 = 5161.75 Hz

n=7, f4 = 7*f1 = 7226.45 Hz