The diameters of the main rotor and tail rotor of a single$-$engine helicopter are $7\mathrm{.}67$ m and $1\mathrm{.}05$ m$,$ respectively. The respective rotational speeds are $448$ rev$/$min and $4,130$ rev$/$min$.$

a. Calculate the speeds of the tips of both rotors. 

b. Compare these speeds with the speed of sound, $343$ m$/$s$.$