Simulation of string vibration

1. A method, comprising:

simulating a string using a wave equation that relates movement of the string in time to force acting on the string, wherein the string has a longitudinal axis in a first direction and is moveable in a second direction orthogonal to the first direction, and the force acting on the string simulates a stream of a fluid medium flowing relative to the string in a direction having a component in a third direction orthogonal to both the first and second directions; and

creating sounds using the wave equation.

2. A method according to claim 1 , wherein the simulated string is supported between two supports, is aligned at rest in the first direction and has a depth in the third direction, whereby the string has a leading edge closer to a source of the stream of fluid medium and a trailing edge further from the source of the stream of fluid medium.

3. A method according to claim 2 , wherein the string is caused from rest to vibrate in a plane, which includes the first and second directions, by turbulence in the fluid flow causing the stream of fluid medium to exert a pressure on the string in the second direction.

4. A method according to claim 2 or claim 3 , wherein:

when the leading and trailing edges are out of alignment with one another, the stream of fluid medium exerts a force on the string in the second direction.

5. A method, comprising:

simulating a string using a wave equation that relates movement of the string in time to force acting on the string, wherein

the string has a longitudinal axis in an x-direction and a depth in a z-third direction orthogonal to the x-direction;

the string is supported between two supports whereby it is aligned at rest in the x-direction and is moveable in a y-direction orthogonal to the x- and z-directions;

and the force acting on the string simulates a stream of a fluid medium flowing relative to the string in a direction having a component in a z-direction, whereby the string has a leading edge closer to a source of the stream of fluid medium and a trailing edge further from the source of the stream of fluid medium; and

creating sounds using the wave equation.

6. A method according to claim 5 , wherein the string comprises a plurality of discrete elements aligned at rest in the x-direction and spaced apart by a distance dx, each element having a depth dz; and

the leading and trailing edges of the discrete elements are able to move in discrete steps of time dt in the y-direction only.

7. A method according to any one of claims 1 , 2 , 3 , 5 , or 6 , wherein the wave equation is an approximation of the continuous wave equation

M

⁢

∂

2

⁢

y

∂

t

2

=

T

⁢

∂

2

⁢

y

∂

x

2

-

S

⁢

∂

4

⁢

y

∂

x

4

+

L

T

⁢

∂

3

⁢

y

∂

x

2

⁢

∂

t

-

L

s

⁢

∂

5

⁢

y

∂

x

4

⁢

∂

t

-

L

v

⁢

∂

y

∂

t

+

F

⁡

(

x

,

t

)

in which:

F(x, t) denotes an external force at coordinate x on the string at time to

M denotes mass per length;

S denotes stiffness of the string;

T denotes tension of the string;

Ls denotes a loss associated with the stiffness of the string;

Lt denotes a loss associated with the tension of the string; and

Lv denotes a loss associated with the turbulent flow of the fluid medium.

8. A method according to claim 7 , in which the string comprises a plurality of j discrete elements from j=0 at one end supported by a first support to j=x−1 at the opposite end supported by a second support; wherein j is an integer; and

the stream of fluid medium flows at least partly in the z-direction and exerts a pressure on the elements of the string.

9. A method according to claim 8 , wherein the force F PRESz [n, j] at time n acting on an element j due to the pressure on the string is given by;

F PRESz [n,j]=P z *( C (( y[n,j]−y[n− 1 ,j ])/ dz ))/ dt 2 *W ( j,y[n,j ])

in which:

P z denotes the pressure exerted by the stream of fluid 30 on the lamella;

C((y[n, j]−y[n−1, j])/dz) denotes a function of (y[n, j]−y[n−1, j])/dz in respect of the dependency of the force acting on each element j due to the torsion of the lamella; and

W(j, y[n, j]) denotes a weighting function representing the intensity of the stream of fluid depending on the current x- and y-position of the element j under consideration.

10. A method according to claim 8 , wherein the approximation of the continuous wave equation is the discrete recursion formula:

y[n+ 1 ,j ]=( y[n,j− 2 ]·c 1 +y[n,j− 1 ]·c 2 +y[n,j]·c 3 +y[n,j+ 1 ]·c 2+ y[n,j+ 2 ]·c 1 +y[n− 1 ,j− 2]· c 4 +y[n− 1 ,j− 1 ]·c 5 +y[n− 1 ,j]·c 6 +y[n 1, j+ 1 ]·c 5 +y[n− 1 ,j+ 2] ·c 4)/ M[j]+ 2 y[n,j]+F[n,j]/M[j]

in which:

dx=1;

dt=1;

y[n, j] denotes the excursion of discrete element j in the y-direction at time n;

y[n+1, j] denotes the excursion of discrete element j in the y-direction at time n+1;

y[n, j+1] denotes the excursion of discrete element j+1 in the y-direction at time n;

M[j] denotes the mass of discrete element j;

F[n, j] denotes an additional external force acting on a discrete element j at time n; and

c1 to c6 are coefficients, which depend on the material parameters of the string and the surrounding media.

11. A method according to claim 10 , wherein

c 1=−( S+Ls );

c 2 =T+ 4 S+Lt+ 4 Ls;

c 3=−(2 T+ 6 S+Lv+ 2 Lt+ 6 Ls );

c4=Ls;

c 5=−( Lt+ 4 Ls ); and

c 6 =Lv+ 2 Lt+ 6 Ls.

12. A method according to claim 10 , wherein when dz=1 the force F PRESz [n, j] at time n acting on an element j due to the pressure on the string is given by:

F PRESz [n,j]=P z *( C ( y[n,j]−y[n− 1 ,j ]))* W ( j,y[n,j ])

in which:

P z denotes the pressure exerted by the stream of fluid 30 on the lamella;

C((y[n, j]−y[n−1, j])/dz) denotes a function of (y[n, j]−y[n−1, j])/dz in respect of the dependency of the force acting on each element j due to the torsion of the lamella; and

W(j, y[n, j]) denotes a weighting function representing the intensity of the stream of fluid depending on the current x- and y-position of the element j under consideration.

13. A method according to claim 12 , wherein the force F TURB [n, j] at time n acting on an

F TURBz [n,j]=C TURBz *W TURB ( j,y[n,j ])* N RND [n]

in which

C TURBz denotes a turbulence coefficient;

N RND [n] denotes a random signal; and

W TURB (j, y[n, j]) denotes a weighting function representing intensity of the turbulence in the air jet depending on the current x- and y-position of element j under consideration.

14. A method according to claim 13 , wherein the random signal comprises a low pass filtered noise.

15. A method according to claim 13 , wherein the total force at time n acting on an element

F z [n,j]=F PRESz [n,j]+F TURBz [n,j].

16. A method according to claim 12 , in which the fluid flow is orthogonal to the x-direction but at an angle beta to the z-direction, wherein the equation for force is modified to:

F zactual =F z cos(beta).

17. A method according to claim 10 , wherein the elements at the supports are not movable so y=0 for these elements and the discrete recursion formula is solved for the elements adjacent the respective supports by providing a dummy element at opposite ends of the string so that the excursion y[n+1, −1] of a dummy element j=−1 adjacent one support for the next discrete time n+1 is given by:

y[n+ 1,−1]=− y[n+ 1,1]

and the excursion y[n+1, x] of a dummy element j=x adjacent the other support for the next sample n+1 is given by:

y[n+ 1 ,x]=−y[n+ 1, x− 2].

18. A method according to claim 5 , wherein the elements at the supports do not move.

19. A method according to claim 5 , wherein a support at one end of the string and the corresponding element are moveable in the y-direction.

20. A method according to any one of claim 1 to 3 , wherein the force acting on the string further simulates a stream of fluid flowing relative to the string in a direction having a component in the first direction.

21. A method according to claim 5 , wherein the force acting on the string further simulates a stream of fluid flowing relative to the string in a direction having a component in the x-direction.

22. A method according to any one of claims 1 , 2 , 3 , or 5 , further comprising generating a sound based on movement of the simulated string.

23. An apparatus for performing a method according to any one of claims 1 to 3 and 5 .

24. An apparatus according to claim 23 , wherein the apparatus comprises a computer.

25. An apparatus according to claim 24 , wherein the apparatus further comprises a loudspeaker.

26. A sound synthesiser comprising an apparatus according to claim 23 .

27. A machine-readable medium containing a computer program for causing a computer to carry out the method according to any one claims 1 to 3 and 5 .

28. A storage medium storing a computer program according to claim 27 .

29. A machine readable medium containing executable program instructions which when executed on a data processing system cause the data processing system to perform a method comprising:

simulating a string using a wave equation that relates movement of the string in time to a force acting on the string, wherein the string has a longitudinal axis in a first direction and is moveable in a second direction orthogonal to the first direction,

simulating a stream of fluid medium flowing relative to the string in a direction having a component in a third direction orthogonal to both the first and the second directions to provide the force acting on the string; and

producing data from the simulating to create sounds.

30. A machine readable medium as in claim 29 wherein the method further comprises:

producing the sounds through a speaker.