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  4. 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?

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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?

JIPMERJIPMER 2006Waves

Solution:

Each tuning forck gives 3 beats with the next, so the difference in the frequencies of two consecutive forks is 3 .
$\therefore f_{26} =f_{1}+(n-1) \times-3$
$f =2 f+(26-1) \times-3$
$f =75\, Hz .$
$\therefore $ Frequency of 18 th tuning fork
$f_{18} =f_{1}+(18-1) \times-3$
$=2 \times 75+17 \times-3$
$=150-51=99\, Hz$.