Question

Determine the frequency of the 2nd harmonic of a spring that has a 3rd harmonic resonance of f3=512 Hz.

Answer 1

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

$f_n = nf_1$

where

n is the number of the harmonic

$f_1$ is the fundamental frequency

Here we have:

$f_3=512 Hz$ is the frequency of the 3rd harmonic

So the fundamental frequency is

$f_1=\frac{f_3}{3}=\frac{512}{3}=170.7 Hz$

And so, the frequency of the 2nd harmonic is:

$f_2=2f_1=2(170.7)=341.3 Hz$