# Multiples of natural frequency?

1. Oct 30, 2010

### LoveKnowledge

Multiples of natural frequency??

Hi all! I am a little confused. Why will an object not resonate with multiples of its natural frequency?

I think due to the reason that through its multiples, it will not return (even if temporarily) to its natural state...am I mistaken??

2. Oct 30, 2010

### sophiecentaur

Re: Multiples of natural frequency??

Can you think of a reason why is should? What are the conditions for resonance?
There is no reason why an 'ideal' mass on an 'ideal' spring should resonate at any more than one frequency.
If you are thinking about a structure which is based on standing waves, then the geometry and the physical details may well not mean that multiple nodes would be sustained at harmonics of the fundamental. This is why they are given the name 'overtones', to avoid confusion.
For this ideal behaviour you need the speed of waves to be independent of the frequency (a special case) and the ends to be ideal reflectors of the waves which are going back and forth.
Consider a disc of metal. The modes of vibration are very complex and you can produce all sorts of resonances over the two dimensional surface. I believe that this may be a good reason why cymbals are made circular so that they produce a very random-like response to being bashed - with no particular audible 'note'.
Take a very familiar case of water waves in a trough. There is no harmonic relationship at all between the frequencies of the different resonance modes. Try it in the bath next time - when the rubber duck ceases to be fun Try not to get the stopwatch wet, though.

3. Oct 30, 2010

### LoveKnowledge

Re: Multiples of natural frequency??

thx for your explanation. it clarifies things up a bit (I understand it 85% now) but just a little confused still.

4. Oct 30, 2010

### sophiecentaur

Re: Multiples of natural frequency??

For a 'perfect' string, your ideas hold.
But it gets more complicated as soon as you go away from 'ideal'.