Answer:
1) 341 Hz
Explanation:
When a string vibrates, it can vibrate with different frequencies, corresponding to different modes of oscillations.
The fundamental frequency is the lowest possible frequency at which the string can vibrate: this occurs when the string oscillate in one segment only.
If the string oscillates in n segments, we say that it is the n-th mode of vibration, or n-th harmonic.
The frequency of the n-th harmonic is given by
[tex]f_n = nf_1[/tex]
where
n is the number of the harmonic
[tex]f_1[/tex] is the fundamental frequency
Here we have:
[tex]f_3=512 Hz[/tex] is the frequency of the 3rd harmonic
So the fundamental frequency is
[tex]f_1=\frac{f_3}{3}=\frac{512}{3}=170.7 Hz[/tex]
And so, the frequency of the 2nd harmonic is:
[tex]f_2=2f_1=2(170.7)=341.3 Hz[/tex]
