Q. There are 26 tuning forks arranged in the decreasing order of their frequencies. Each tuning fork gives 3 beats with the next. The first one is octave of the last. What is the frequency of 18th tuning fork?

Solution:

Frequency of two consecutive forks is 3.
$\therefore f =f_1 + (n-1) (d)$ (arithmetic progression)
Given, $ \, \, \, \, \, f_1 = 2 f, n = 26 , d = -3 $
$\therefore \hspace20mm f = 2 f + (26 - 1)(-3)$
$\hspace30mm f = 75 Hz$
Frequency of 18th tuning fork is
$\hspace30mm f _{18} = f_1 + (18-1)(-3)$
$\hspace30mm = 2 \times 75 + 17 \times (-3)$
$\hspace30mm = 150 - 51 = 99 \, Hz$

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