write code to model acoustic wave propagation underwater in javascript

Modeling acoustic wave propagation underwater requires solving partial differential equations (PDEs) of acoustic wave equations. Specifically, the Helmholtz equation, which is a second-order linear partial differential equation.

In order to implement an acoustic wave propagator model in JavaScript, we need to discretize the Helmholtz equation using finite difference method. The finite difference method approximates the continuous derivatives in the equation by differences between discrete grid points.

Here's an example implementation of the Helmholtz equation in 2D using a finite difference method in JavaScript:

index.tsx
const c = 1500; // speed of sound in water
const dt = 0.001; // time step
const dx = 1; // spatial step
const N = 100; // number of grid points in one dimension
const f0 = 500; // frequency of source
const source = [N/2, N/2]; // location of source
const tEnd = 0.5; // end time

// initialize velocity and pressure fields
let u = new Array(N*N).fill(0);
let u1 = new Array(N*N).fill(0);
let u2 = new Array(N*N).fill(0);
let p = new Array(N*N).fill(0);

// initialize source function in time domain
const tSrc = Array.from({length: Math.ceil(tEnd/dt)}, (_, i) => i*dt);
const src = tSrc.map(t => Math.sin(2*Math.PI*f0*t));

// main loop for wave propagation
for (let n = 0; n < tSrc.length; n++) {
  // update velocity field
  for (let i = 1; i < N-1; i++) {
    for (let j = 1; j < N-1; j++) {
      u1[i*N+j] = u[i*N+j] - c*c*dt/dx*(p[i*N+j+1] - p[i*N+j] + p[i*N+j+N] - p[i*N+j]);
    }
  }
  // update pressure field
  for (let i = 1; i < N-1; i++) {
    for (let j = 1; j < N-1; j++) {
      p[i*N+j] = p[i*N+j] - c*c*dt/dx*(u1[i*N+j] - u1[i*N+j-1] + u1[i*N+j-N] - u1[i*N+j]) + src[n]*dt;
    }
  }
  // update velocity field
  for (let i = 1; i < N-1; i++) {
    for (let j = 1; j < N-1; j++) {
      u2[i*N+j] = u1[i*N+j] - c*c*dt/dx*(p[i*N+j] - p[i*N+j-1] + p[i*N+j-N] - p[i*N+j]);
    }
  }
  // update velocity field for next time step
  for (let i = 0; i < N*N; i++) {
    u[i] = u2[i];
  }
}
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This code uses a simple finite difference method to model the 2D wave propagation over an N by N grid of points. The wave speed c and the grid spacing dx are specified along with the time step dt used for numerical simulation. The pressure field is calculated from the velocity field, which is updated using the pressure field of the previous time step.

This code can be modified to create more complex models with varying environments, such as including obstacle interactions, or changing wave properties. Ultimately, the complexity of the model will depend on the specific features and environment relevant to the problem being solved.

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