Question

41 tuning forks are so arranged that every tuning fork generates 5 beat/s to its nearest tuning fork. The frequency of the last tuning fork is double the frequency of first tuning fork. Calculate the frequency of first and last tuning fork.

Answer 1

Let the frequency of first fork = x
As each fork generates 5 beats/s to its nearest fork, thus it will be in A.P.
Thus for u/st fork = [α + (n – 1) × 5]
Given n = 41, 5
⇒ = [x + (41 - 1) × 5]
= x + 200
As per question,
frequency of last fork = 2 × frequency of first fork
x + 200 = 2x
2x – x = 200
x = 100 Hz
∴ Frequency of first fork = 100 Hz frequency of last fork = 2 × 100 = 200 Hz