A commuter train passes a passenger platform at a constant speed of $39\mathrm{.}1$ m$/$s$.$ The train horn is sounded at its characteristic frequency of $340$ Hz$.$

$($a$)$ What overall change in frequency is detected by a person on the platform as the train moves from approaching to receding? $($Indicate whether the frequency increases of decreases with the sign of your answer.$)$

Hz

$($b$)$ What wavelength is detected by a person on the platform as the train approaches?

m