A 160 cm long string has two adjacent resonances at frequencies of 85 Hz and 102 Hz. What is the fundamental frequency of the spring?

The lowest frequency produced by any particular instrument is known as the fundamental frequency. The fundamental frequency is also called the first harmonic of the instrument

The frequency of the nth harmonic (where n represents the harmonic # of any of the harmonics) is n times the frequency of the first harmonic.

In equation form

[math] f_n = n f_1[math]

Adjacent resonances 85 Hz and 102 Hz

                                  f_n=85Hzfn​=85Hz      

  write the integral multiple of the numbers 85 and 102

                            85 = 17 * 5  ( f_n = n f_1fn​=nf1​ here n = 5, f_1 = 17 f1​=17)

                            102 = 17  * 6    ( f_n = n f_1fn​=nf1​ here n = 6, f_1 = 17 f1​=17)

Hence,

The fundamental frequency f_1f1​ =  17