  We investigate the lifespan of solutions to a specific variant of the
semilinear wave equation, which incorporates weighted nonlinearity $$
u_{tt}-u_{xx} =|x|^\alpha |u|^p, \quad\mbox{for}\;\;\; (t,x)\in
(0,\infty)\times\mathbb{R}, $$ where $p>1$, $\alpha\in\mathbb{R}$. We explore
the behavior of solutions for small initial data, considering the influence of
weighted nonlinearities on the lifespan.
