# 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?

BHUBHU 2005Electromagnetic Waves

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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