Question

A set of 25 tuning forks is arranged in order of decreasing frequencies. Each fork produces 3 beats with succeeding one. If the first fork is octave of last, then the frequency of 1st and 15th fork in Hz is ______.

पर्याय

• 144, 99

• 72, 99

• 144, 102

• 72, 102

Answer 1

A set of 25 tuning forks is arranged in order of decreasing frequencies. Each fork produces 3 beats with succeeding one. If the first fork is octave of last, then the frequency of 1st and 15th fork in Hz is 144, 102.

Explanation:

n₁ - n₂ = 3   ∴ n₁ - n₂ = - 3

n₂ - n₃ = 3   n₃ = n₂ - 3 = n₁ - 6 = n₁ - 2 · 3 = n₁ - (3 - 1) · 3

n₂₅ = n₁ - (25 - 1) · 3

`"n"_1/2 = "n"_1 - 72`

∴ n₁ = 72 × 2 = 144 Hz

n₁₅ = 144 - 14.3 = 144 - 42 = 102 Hz