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?

Question

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? (A) 100 Hz (B) 99 Hz (C) 96 Hz (D) 103 Hz

Tardigrade Admin · Accepted Answer

Each tuning forck gives 3 beats with the next, so the difference in the frequencies of two consecutive forks is 3 .

∴ f_{26} = f_{1} + (n - 1) \times - 3

f = 2 f + (26 - 1) \times - 3

f = 75 Hz .

∴

Frequency of 18 th tuning fork

f_{18} = f_{1} + (18 - 1) \times - 3

= 2 \times 75 + 17 \times - 3

= 150 - 51 = 99 Hz

.

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?

100 Hz

99 Hz

96 Hz

103 Hz

Each tuning forck gives 3 beats with the next, so the difference in the frequencies of two consecutive forks is 3 . ∴f26​=f1​+(n−1)×−3 f=2f+(26−1)×−3 f=75Hz. ∴ Frequency of 18 th tuning fork f18​=f1​+(18−1)×−3 =2×75+17×−3 =150−51=99Hz.

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?