56 tuning forks are so arranged in series that each fork gives 4 beats per sec with the previous one. The frequency of the last fork is 3 times that of the first. The frequency of the first fork is

Let the frequency of first fork be n, then the frequency of last fork be 3 n. As each fork gives 4 beats with previous
one, hence frequencies are

 $$\begin{gathered} \mathrm{n},(\mathrm{n}+4),(\mathrm{n}+2\times 4),\dots ,3\mathrm{n} \\ \mathrm{t} \mathrm{forms} \mathrm{an} \mathrm{A}.\mathrm{P} \\ {\mathrm{a}}_{\mathrm{n}}=\mathrm{a}+(\mathrm{n}-1)\mathrm{d} \\ 3\mathrm{n}=\mathrm{n}+(56-1)4 \\ 2\mathrm{n}=220\text{ or }\mathrm{n}=110 \end{gathered}$$