Question

A set of $20$ tuning forks is arranged in a series of increasing frequencies. If each fork gives $4$ beats with respect to the preceding fork and the frequency of the last fork is twice the frequency of the first, then the frequency of last fork is ____$Hz$.

Answer 1

$f_{1}=f$
$f_{2}=f+4 $
$f_{3}=f+2 \times 4 $
$f_{4}=f+3 \times 4 $
$f_{20}=f+19 \times 4 $
$f+(19 \times 4)=2 \times f$
$ f=76\, Hz .$
Frequency of last tuning forks $=2 f$
$=152 \,Hz$