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 #2n and n# respectively.

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#