Answer
Mandy hears a beat frequency of $~6.4~Hz$
Work Step by Step
We can use the equation for the Doppler effect when the observer is approaching:
$f_1 = \left(\frac{v+v_o}{v}\right)~f_s$
$f_1 = \left(\frac{343~m/s+1.56~m/s}{343~m/s}\right)~(698~Hz)$
$f_1 = 701.2~Hz$
We can use the equation for the Doppler effect when the observer is moving away:
$f_2 = \left(\frac{v-v_o}{v}\right)~f_s$
$f_2 = \left(\frac{343~m/s-1.56~m/s}{343~m/s}\right)~(698~Hz)$
$f_2 = 694.8~Hz$
The beat frequency is the difference between the two frequencies that Mandy hears from the sirens. We can find the difference of the two frequencies:
$f_1-f_2 = 701.2~Hz-694.8~Hz = 6.4~Hz$
Mandy hears a beat frequency of $~6.4~Hz$.
