Formation of Beats

A set of 12 tuning forks is arranged in order of increasing frequencies. Each fork produces Y beats per second with the previous one. The last is an octave of the first. The fifth fork
has a frequency of 90 Hz. Find Y and frequency of the first and the last tuning forks.

A set of 48 tuning forks is arranged in a series of descending frequencies such that each fork gives 4 beats per second with preceding one. The frequency of first fork is 1.5 times the frequency of the last fork, find the frequency of the first and 42^nd tuning fork

Let n₁ and n₂ be the two slightly different frequencies of two sound waves. The time interval between waxing and immediate next waning is ______.

(A) `1/(n_1-n_2)`

(B) `2/(n_1-n_2)`

(C) `(n_1-n_2)/2`

(D) `1/(2(n_1-n_2))`  

A sonometer wire is in unison with a tuning fork of frequency 125 Hz when it is stretched by a weight. When the weight is completely immersed in water, 8 beats are heard per second. Find the specific gravity of the material of the weight.

A train blows a whistle of frequency 640 Hz in air. Find the difference in apparent frequencies of the whistle for a stationary observer, when the train moves towards and away from the observer with the speed of 72 Km/hour. [Speed of sound in air = 340 m/s.]