4.1 Internal Sounds in Brass Instruments
105
0
500
1000
1500
2000
2500
Axial distance (mm)
-1
0
1
Pressure (arb. units)
(a)
(b)
(c)
Fig. 4.4 Sinusoidal sound wave travelling down a cylindrical tube. (a) Time t = 0 ms. (b) Time
t = 2.15 ms. (c) Time t = 8.05 ms
1989). At this stage we neglect energy losses due to the viscosity of air (see
Sect. 4.7). The linear acoustic wave equation then takes the form
p =
1
c 2
∂ 2 p
∂t 2 ,
(4.1)
where is the Laplacian operator. In a three-dimensional Cartesian coordinate
system x, y, z, Eq. 4.1 can be written as
105
0
500
1000
1500
2000
2500
Axial distance (mm)
-1
0
1
Pressure (arb. units)
(a)
(b)
(c)
Fig. 4.4 Sinusoidal sound wave travelling down a cylindrical tube. (a) Time t = 0 ms. (b) Time
t = 2.15 ms. (c) Time t = 8.05 ms
1989). At this stage we neglect energy losses due to the viscosity of air (see
Sect. 4.7). The linear acoustic wave equation then takes the form
p =
1
c 2
∂ 2 p
∂t 2 ,
(4.1)
where is the Laplacian operator. In a three-dimensional Cartesian coordinate
system x, y, z, Eq. 4.1 can be written as