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 $18^{t h}$ tuning fork?

100 H z

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99 H z

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96 H z

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103 H z

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Solution

The correct option is B $99 H z$
Let the frequency of first tuning fork is $υ$ . The frequencies of other tuning forks are
$(υ - 3), (υ - 2 \times 3), . . . . . ., (υ - 17 \times 3), . . . . ., (υ - 25 \times 3)$ .
As per given condition,
$υ = 2 (υ - 25 \times 3)$ or $υ = 2 υ - 25 \times 6$
or $υ = 25 \times 6 = 150 H z$
The frequency of the $18^{t h}$ tuning fork
$υ - 17 \times = 150 - 51 = 99 H z$

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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?

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 $18^{t h}$ tuning fork?