Wave propagation simulations are foundational tools across scientific and medical applications, yet their computational demands become significant for high-resolution simulations, particularly in medical applications where precise representation of different tissue geometries is crucial. This paper presents a novel approach to accelerate 2D wave propagation simulations in the k-Wave toolbox. Our method focuses on optimising Fourier transform computations through spectrum pruning. The Acoustic Field Propagator along with a bisection pruning algorithm to estimate the position of the spectral coefficients is used. Through these optimisations, our approach achieves significant performance gains, demonstrating speedups of up to 1.8x for large simulation domains. Experimental evaluation on medical ultrasound simulations demonstrates that the proposed method achieves focal point errors below 1% with minimal focus position shifts, while skipping up to 90% of spectral coefficients in large domains. This results in a significant simulation time reduction by half over the large simulation domains. Although the proposed method primarily focuses on accelerating k-Wave toolbox wave propagation simulation, it could be generally applied to wave propagation problems.