As an earthquake starts, you are standing \(150 \mathrm{~km}\) (as the wave travels) from the epicenter. A geophysicist near the epicenter immediately telephones you to let you know that the transverse wave from the earthquake is on its way to you and that it is described by the equation

\[f(x, t)=a \sin (b x-\omega t),\]

where \(a=0.560 \mathrm{~m}, b=0.0157 \mathrm{~m}^{-1}\), and a full wavelength passes any given location every \(0.500 \mathrm{~s}\). How long will it be before the ground you are standing on starts to shake?