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# 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?

one year ago

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