Question

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

a.341 Hz


b.768 Hz


c.1536 Hz


d.512 Hz

Answer 1

1) 341 Hz

Step-by-step 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=(f_3)/(3)=(512)/(3)=170.7 Hz`

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

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