Q88 / 160 · JIPMER 2006 · Physics

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 18 th tuning fork?

  • A
    100 Hz
  • Correct answer
    B
    99 Hz
  • C
    96 Hz
  • D
    103 Hz

Solution

Each tuning forck gives 3 beats with the next, so the difference in the frequencies of two consecutive forks is 3 . $\begin{aligned} \therefore \quad f_{26} & =f_1+(n-1) \times-3 \\ f & =2 f+(26-1) \times-3 \\ f & =75 \mathrm{~Hz} .\end{aligned}$ $\therefore$ Frequency of 18 th tuning fork $\begin{aligned} f_{18} & =f_1+(18-1) \times-3 \\ & =2 \times 75+17 \times-3 \\ & =150-51=99 \mathrm{~Hz}\end{aligned}$

Hence, the correct answer is option: 'B'.

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