Date: Tue, 2 Mar 1999 17:17:18 -0500 (EST)
Author: Steve Wonnell
Subject: Re: Missing Fundamental
I'm not sure that I clearly understand the description of your
apparatus, but it seems to me that you have not yet eliminated
the fundamental. If you generate a sound wave at 768 Hz,
and also a sound wave at 512 Hz, you will also generate a sound
wave at 256 Hz because of the beat. This is a real, physical
sound wave that you can detect with a microphone and fourier
I assume that you're trying to generate a situation where a person
perceives the 256 fundamental without there actually being
a measurable sound at that frequency, right?
One suggestion...how about producing a circuit that generates the 256 Hz
sound wave with all the harmonics, and then adding a second circuit with
only the pure 256 Hz signal, 180 out of phase and at the same amplitude?
This ought to generate the correct sound wave. Maybe you can do
this using the Pasco Fourier Synthesizer???
Easier said than done, of course
By the way...I came across a reference to your 1981 article on a Capstan
experiment...haven't yet read your article...this was in a 1991 article by
Eugene Levin on the relationship between friction and the number of turns
a rope is wrapped around a post. Interesting stuff...a faculty member is
developing a "quickie" experiment on this topic.
On Tue, 2 Mar 1999, Clifford Bettis wrote:
> Date: Tue, 02 Mar 1999 15:53:42 -0600
> From: Clifford Bettis
> To: "email@example.com"
> Subject: Missing Fundamental
> Hi all,
> I've been asked to supply a demonstration for a colloquium on musical
> acoustics. Specifically, the speaker wants to show the fact that if you
> generate all the harmonics of a given frequency and leave out the
> fundamental, you will still hear the fundamental, even though it's not
> there physically.
> What I am trying and having some success with is this: I use two
> oscillators connected to speakers through diodes. One is tuned to 512
> Hz, the other, 768 Hz. The diodes are to generate the harmonics. So I
> should have all the harmonics of 256 Hz without the fundamental. I do
> "hear" the 256 Hz missing fundamental, but I would like it to be more
> obvious. I did find using a 256 Hz fork as a reference a help in tuning
> and showing passersby what to listen for.
> Does anyone have any advice for me?
> Cliff Bettis