A horizontal rope of length \(L\) is held under uniform tension \(F_T\). The linear mass density of the rope increases linearly from \(\mu_0\) at \(x = 0\) to \(3\mu_0\) at \(x = L\). A continuous wave generator at \(x = 0\) drives the rope, sending waves toward \(x = L\). To estimate the transit time \(\Delta t\) of a wave pulse along the rope, a student uses the wave speed calculated at the rope's average linear mass density \(\mu_{\text{avg}}\). Which choice correctly states the expression for the estimated transit time \(\Delta t\) and describes the behavior of the wave frequency \(f\) as the wave travels toward \(x = L\)?