$25$ 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 $21$ st fork is :

72

No worries! We‘ve got your back. Try BYJU‘S free classes today!

288

No worries! We‘ve got your back. Try BYJU‘S free classes today!

87

No worries! We‘ve got your back. Try BYJU‘S free classes today!

84

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $84$ Hz
Let the frequency of the last fork be $n$ .

Therefore, the frequency of the 1st fork is $2 n$ and any two successive forks produce 3 beat/s

The frequency of the 2nd fork will be
$2 n - 3$ .

Frequency of the 3rd fork will be, $2 n - 6$

Now, the frequency of the 25th fork will be,

$2 n - (25 - 1) \times 3 = n$

$2 n - 72 = n$

$n = 72 H z$

The frequency of 1st fork will, $2 n = 2 \times 72 = 144 H z$

The frequency of 21st fork is,

$f = 2 n - (21 - 1) \times 3$

$f = 144 - 20 \times 3$

$f = 144 - 60 = 84 H z$

The correct option is D.

Suggest Corrections

Similar questions

25

tuning forks are arranged in decreasing order of frequency. Any two successive forks produce

3

beats/sec. If the frequency of the first tuning fork is the octave of last, then the frequency of

21^{s t}

fork is

Q. A set of 12 tuning forks is arranged in the increasing order of frequencies. Each tuning fork produces ‘y’ beats per second with previous one. The last tuning fork is an octave of the first. The fifth tuning fork has frequency 90 Hz. Find ‘y’. Hence find the frequency of the last fork.

Q. 16 tuning forks are arranged in the order of increasing frequencies. Any two successive fork give 8 beats per sec when sounded together. If the last fork gives the octave of the first, then the frequency of the first fork is-

A tuning fork (pair) produces 4 beats/sec with another fork of frequency 288 Hz. A little wax is placed on the unknown fork and it then produces 2 beats/sec. The frequency of the unknown fork is

Q. P, Q and R are three tuning forks. Frequency of tuning fork P is

380 Hz

. Number of beats produced by tuning forks P and Q is

10 Hz

and by tuning forks Q and R is

8 Hz

. When wax is put on P, beat frequency produced by tuning forks P and Q becomes

4 Hz

and by tuning forks P and R becomes

12 Hz

. Frequency of fork Q is greater than the frequency of fork R. Find natural frequency of tuning forks Q and R respectively.

Join BYJU'S Learning Program

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 :

$25$ 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 $21$ st fork is :