Let the unknown frequency be f. Beat frequency b=|f−f′| For f′=250Hzb=4 ∴|f−250|=4......(1) For f′=513b=5 ∴|2f−513|=5......(2) Case 1:2f>513Hz and f>250Hz We get f−250=4⟹f=254Hz and 2f−513=5⟹f=259Hz which is not possible. Case 2: 2f <513Hz and f>250Hz We get f−250=4⟹f=254Hz And 513−2f=5⟹f=254Hz Case 3:2f<513Hz but f<250Hz We get 250−f=4⟹f=246Hz And 513−2f=5⟹f=254Hz Which is not possible. So the unkown frequency f=254Hz