A violin A-string, fixed at both ends, has a certain length and linear mass density. One of the resonance frequencies of the string is 1320 Hz, and the next resonance frequency is 1760 Hz. There are no frequencies between these two.

(a) What is the lowest resonance frequency (fundamental) of the A-string?

In this problem, we're dealing with the resonance frequencies of a violin string. Resonance frequencies are those at which the string vibrates most naturally.

Here, we take into account the fact that there's no resonance frequency between 1320 Hz and 1760 Hz, which informs us that these represent the second and third harmonics (overtones).

As the resonance frequencies are multiples of the fundamental frequency for harmonics (each harmonic is an integer multiple of the fundamental frequency), we discover that the first or lowest resonance frequency (fundamental frequency) can be found by simply dividing the second harmonic frequency by 2. Thus, the fundamental frequency is 1320 Hz / 2 = 660 Hz.

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