Why does a flat, big piece of thin rounded metal vibrate slowly when hit?

Question

This question is asked in relation to a cymbal.

Why is a sound of a low pitch produced when a piece of metal (as described above) is hit compared to a cymbal which is small, thick and has quite a high profile.

When a thin piece of metal is hit, why does it not vibrate quickly compared to a thick piece. Since, it is lighter, it must be easier to move and therefore produce a sound of a high pitch. Why is this not the case?

I can sort of understand why an increase in size means that it vibrates slower but can someone explain it so that I can get it more clear in my mind?

Why does a cymbal with a low profile produce a lower sound than one with a high profile?

Thanks.

Answer 1

If you want the math (and it is tough!!) see Timoshenko's "Theory of Plates and Shells".

Basically, the thicker a piece of metal compared to it's area (a quasi aspect ratio), the "stiffer" and hence the higher the natural frequency.  A thinner piece will thus resonate at a lower frequency.

Think of a "ruler" made out of metal.  The natural frequency gets lower as you lengthen it.  And the natural frequency gets higher as you thicken it.

The same basic properties are at work on a "drum head" or cymbal but in more dimensions.

I know that this is "seat of the pants" and not rigorous physics, but it's a place to start.

-Fred