Question

A set of 8 tuning forks is arranged in a series of increasing order of frequencies. Each fork gives 4 beats per second with the next one and the frequency of last fork is twice that of the first. Calculate the frequencies of the first and the last fork.

Answer 1

Given : n₈ = 2 n₁, beat frequency = 4 Hz

The set of tuning fork is arranged in the increasing order of their frequencies.

∴ n₂ = n₁ + 4

n₃ = n₂ + 4 = n₁+ 2 x 4

n₄ = n₃ + 4 = n₁ +3 x 4

∴ n₈ = n₇ + 4 = n₁ + 7 x 4 = n₁ + 28

Since n₈ =2n₁,

2n₁ = n₁ + 28

 The frequency of the first fork, n₁ = 28 Hz

 The frequency of the last fork,

n₈ = n₁ + 28 = 28 + 28 = 56Hz