A set of 25 tuning forks arranged in series of decreasing frequencies. Each gives 3 beats per second with the succeeding one. The first fork is the octave of the last. The frequency of the sixteenth fork in series is? (Use nth term of A.P)
1 Answer
Apr 5, 2018
The tuning forks are arranged in decreasing frequencies. Therefore, as per given in the question frequencies of first and last tuning forks are
Frequencies in the given arrangement are as follows
#n_1-> 2n#
#n_2-> 2n-1xx3#
#n_3-> 2n-2xx3#
#n_4-> 2n-3xx3#
#.#
#.#
#n_25-> 2n-24xx3#
Imposing given condition we get
#2n-24xx3=n#
#=>n=72#
So, frequency of 16th tuning fork
#n_16=2n-15xx3#
#=>n_16=2xx72−15xx3=99\ Hz#