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Question: There are 26 tuning forks arranged in the decreasing order of their frequencies. Each tuning fork gi...

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 18th18^{th}tuning fork?

A

100 Hz

B

99 Hz

C

96 Hz

D

103 Hz

Answer

99 Hz

Explanation

Solution

Let the frequency of first tuning fork is υ,\upsilon, The frequencies of other tuning forks are

(υ−3),(υ−2×3),.......(υ−17×3),.....(υ−25×3).(\upsilon - 3),(\upsilon - 2 \times 3),.......(\upsilon - 17 \times 3),.....(\upsilon - 25 \times 3). As per given conditions,

υ=2(υ−25×3)orυ=2υ−25×6\upsilon = 2(\upsilon - 25 \times 3)or\upsilon = 2\upsilon - 25 \times 6

Or υ=25×6=150Hz\upsilon = 25 \times 6 = 150Hz

The frequency of the 18th18^{th}tuning fork

=υ−17×3=150−51=99Hz.= \upsilon - 17 \times 3 = 150 - 51 = 99Hz.