A set of 24 tuning fork is arranged in a series of increasing frequencies. If each fork gives 4 beats per second with the preceding one and the last sounds the ocatve of the first, find the frequencies of the first and the last forks.

Explanation

Let frequency of `Ist` tunning fork = `x`
frequency of `II^(nd)` tunning fork = `x+4`
frequency of `III^(rd)` tunning fork = `x+2(4)`
frequency of `IV^(th)` tunning fork = `x+3(4)`
`therefore` Let frequency of `24^(th)` tuunning fork = `x+23(4)`
octave means, (twice in freq.)
`therefore` freq. of `24^(th)= 2** freq.of I^(st)=2x`
`therefore 2x=x+23(4) Rightarrow x=92

freq.of 24^(th)= 2**92=184H_(3)`.