I have a problem of PDE of jumping rope
$\tau \hspace{0.1 cm}u_{tt} = \rho \hspace{0.1 cm} u_{xx}$ and the boundary conditions are forced sine waves as $$ u(0, t) = sin(\omega t) \text{ and } u(1,t) = sin(\omega t) $$, I have solved it by first splitting it to have homogeneous boundary conditions and then solved by eigenfunction expansion, but the problem is that the question asks about why the density is likely to be fixed. this is the questionquestion
