$3.$ A multimode step index fiber with a core diameter of $80m$ and a relative index difference of $0\mathrm{.}015$ is operating at a wavelength of $0\mathrm{.}85m.$ If the core refractive index is $1\mathrm{.}48.$ Determine: $($a$)$ the normalized frequency for the fiber; $($b$)$ the number of guided modes.