How would one go about finding the sound field produced by a vibrating string? I know how to find the vibrations of the string itself, by solving the wave equation, with boundary conditions that correspond to a string thats held fixed at both ends, and an initial condition that corresponds to some stimulus of the string. This question is not about how to solve this PDE, but concerns what an observer would hear at an arbitrary position close to the string.
Let's assume the string is a length L, along the y axis, and v is the speed of sound at STP. The observer is at a distance d, perpendicular to the center of the string, along the x axis. Can I divide the string up into small segments dl, and consider sound as spherical waves radiating from each of these positions?
Thanks in advance for help with this question!