Two students standing \(54.9 \mathrm{~m}\) apart are tossing around footballs designed to whistle while they are airborne.

(a) When student A throws her football toward student B at \(16.0 \mathrm{~m} / \mathrm{s}\), it emits a frequency of \(680 \mathrm{~Hz}\). What frequency is heard by student B?

(b) When student B throws his football toward student \(A\) at \(15.0 \mathrm{~m} / \mathrm{s}\), it emits a frequency of \(670 \mathrm{~Hz}\). What frequency is heard by student A?

(c) If the two footballs are thrown simultaneously, what is the beat frequency?