so we all know that pitch is related to the frequency of the longitudinal wave produced by hitting a snare head. so this pitch, lets call it 400HZ (i know that number is ridiculously off) is the fundamental or the 1st mode of vibration for a single tap. my question is: if i single stroke at a frequency of 800HZ (another ridiculous number) will the drum sound an octave higher? because you are forcing the drum to produce a longitudinal wave at 800HZ but if its natural vibration was at 400HZ then it would not return to its original position in time for your next stroke. so what would happen? sorry if this is in the wrong fourm...

I'm no physicist so I could be completely off on this. I think the drum would sound the same but just a tad bit louder. I figure the 800hz wave would phase out the 400hz wave resulting in a 400hz wave with increased amplitude.

It is an interesting question, and would love to know the real answer.

No. You're not changing the frequency of one single wave. You're producing multiple waves at a frequency of 800HZ. This would in no way alter the frequency of the sound wave coming from the drum.

Example. We know colors are what they are because of the frequency of the wave of light. Now if I were to take a red light (low frequency) and flash it once, it's obviously red. Now let's say I flash this red light at the frequency of purple. Is it going to look purple? Of course not, strobe lights don't change color when you increase the frequency.

To answer your question, if you played a single stroke roll at a ridiculous frequency, you would most likely end up just hearing what seems like a continuous tone coming from the drum. This would not be much different from the natural resonant frequency of the drum, however (assuming every stroke is the same and dismissing all the effects of tension on the head and yada yada yada).

The drum will resonate at its resonant frequency, no matter how fast you hit it. Striking the drum won't make it complete a wave any faster -- you'll just be starting a new wave before the last one is complete.

Changing your numbers just a little bit (so they're in tune), let's call the drum's resonant frequency 440 Hz, which is A4. If you strike the drum 880 times a second, you probably will discern a pitch one octave higher than the drum's resonant frequency, but it won't be the resonance of the drum you're hearing. The drum will still be resonating at 440 Hz from each strike, but the series of impacts will be fast enough that it'll create its own sound pitched an octave above what happens to be the drum's resonant frequency.

Of course, it's not quite that simple. Unlike pitched instruments, a drum doesn't produce a tone at a given frequency with a series of harmonic overtones. Even if the head is tuned to a given fundamental pitch, drums produce overtones that are scattered thickly all over the frequency spectrum. Even if its strongest resonance is 440 Hz, our drum would be producing waves at just about every audible frequency.

Sound waves are actually compression waves. The others are right. The pitch the head is tuned to is fixed. Striking a drum harder, faster, or somewhere besides the center can produce overtones, these overtones are vibrating in "concert" with the fundamental. In a wind rehearsal I have gotten my winds so "in tune" that the band room has resonated the perfect fifth above the pitch. Also volume is tied to amplitude, which is an indication of how much energy a given wave may have.