Question

If two successive overtones of a vibrating string are 400 hz and 480 hz , what is the frequency of the fundamental?

Answer 1

The general frequency of the nth-overtone is given by

`f_n = n f_1`
where
`f_1` is the fundamental frequency of the string.

If we have two succesive overtones, (n) and (n+1), the difference between their frequencies is

`f_(n+1) - f_n = (n+1) f_1 - nf_1 = nf_1 + f_1 - nf_1 = f_1`
so, the difference between their frequencies is equal to the fundamental frequency.

Therefore, in this problem, the fundamental frequency of the string is simply the difference between the frequencies of the two succesive overtones:

`f_1 = 480 Hz - 400 Hz = 80 Hz`