$32\mathrm{.}41$ In a certain experiment, a radio transmitter emits sinusoidal electromagnetic waves of frequency $110\mathrm{.}0$ MHz in opposite directions inside a narrow cavity with reflectors at both ends, causing a standing$-$wave pattern to occur. $($a$)$ How far apart are the nodal planes of the magnetic field? $($b$)$ If the standing$-$wave pattern is determined to be in its eighth harmonic, how long is the cavity?