Question

A set of 24 tunning forks is arranged in a series of increasing frequencies. If each fork gives 4 beats per second with the preceding one and the last sounds the octave of the first. Find the frequencies of the first and the last forks.

(a) 184 Hz, 92 Hz

(b) 92 Hz, 184 Hz

(c) 85 Hz, 162 Hz

(d) 162 Hz, 85 Hz

Answer 1

Correct option is (b) 92 Hz, 184 Hz

Let, frequency of 1st fork = v

frequency of 2nd fork = v + 4

So, frequency of 24th fork = v + 23 x 4

But frequency of last is the octave of 1st,

\(\therefore\) 2v = v + (23 x 4)

⇒ v = 92 Hz

Frequency of last fork = 2v = 184 Hz