25 tuning forks are arranged in series in the order of decreasing frequency. Any two successive forks produce 3 beats/s. If the frequency of the first tuning fork is the octave of the last fork, then the frequency of the 21st fork is:

Question

25 tuning forks are arranged in series in the order of decreasing frequency. Any two successive forks produce 3 beats/s. If the frequency of the first tuning fork is the octave of the last fork, then the frequency of the 21st fork is: (A) 72 Hz (B) 288 Hz (C) 84 Hz (D) 87 Hz

Tardigrade Admin · Accepted Answer

If n is the frequency of last fork then frequency of first fork be 2n . So, 2n-(25-1)× 3=n ⇒ n=72 Hz 21st fork frequency =144-(21-1)(3) =84 text Hz

Q. 25 tuning forks are arranged in series in the order of decreasing frequency. Any two successive forks produce 3 beats/s. If the frequency of the first tuning fork is the octave of the last fork, then the frequency of the 21st fork is:

72 Hz

288 Hz

84 Hz

87 Hz

144 Hz

If n is the frequency of last fork then frequency of first fork be $2 n$ .
So, $2 n - (25 - 1) \times 3 = n$
$\Rightarrow$ $n = 72 Hz$
21st fork frequency
$= 144 - (21 - 1) (3)$
$= 84 Hz$