Class 11 NEET Physics Waves Questions Questions

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