Understanding the frequency

I am trying to learn more about the frequency and sound and i came up with below thoughts.

The frequency is defined by number of repetitions per second.
For example 1Hz is 1 repetition of the same wave pattern over 1 second, 40hz is forty repetitions of same wave patter over 1seconds, 100hz is one hundred repetitions per second and so on. If I correctly understand the smallest wave pattern would be some change in the air pressure that propagates over the air. For the 40hz signal to happen the air pressure would change in same fashion 40 times over 1 second.
When 40hz is recorded over .5sec we can still hear the 40hz sound. but over shorter time.
Can we say that it is still a 40Hz signal that consists of specific wave pattern that contributes to the 40hz frequency.
Can 1/40 of that signal be called a 40hz frequency signal?
Can we say that the 40Hz signal is that one specific change of the air pressure and it does not matter if it happens 40times per second or 1 time and it is still considered a 40Hz signal?

Now, lets say we have three different signals coming from different locations: 40hz, 100hz and 10000hz. If we record them separately they all would look like repeating wave with specific wave pattern making up its frequency. Now, if we record all three sounds all together the recorded sound waves would be a sum of all three signals that would create much complicated wave pattern and therefore different air pressures propagating over the air.

When the audacity performs the spectrum analysis of the recorded combined signal does it use the Fourier transform to decode different frequencies from the sum of all ? In primitive words, does it scan for patterns repeating over one second time frame and later assigns them to the specific frequency based of number of repetitions in 1 second?

Can we say that the recorded signal - in its finest form - which depends on the sampling frequency is just the amplitude (air pressure) sample at any given time?

It’s not enough for the air to change. That’s call wind. The air needs to Do Something, Do the Opposite thing, and then return to the starting point. Then, if you believe your Fourier work, it needs to repeat that at least twice or three times. Once could be an error or chance impulse indistinguishable from noise. By the third time you have premeditated, intentional sound.

So you should be careful about the assumptions you make on a single cycle of wave.


Agreed. i meant movement in both directions from air rest state.

it does not matter if it happens 40times per second or 1 time and it is still considered a 40Hz signal?

It’s a 40Hz signal, but it’s not sound. It won’t be sound for another three or four cycles.

I don’t know if you’ve ever had the odd experience generating musical tones. You can’t just turn them on and off like a light switch. The leading edge of one cycle of wave is an impulse and contains all frequencies. It’s only when the thing gets rolling through multiple cycles that it turns into a musical tone and drops all its infinite frequency baggage.

It’s a real effect. Pipe organs have “chiff” which describes the delay between the time the air starts and a recognizable tone comes out of a pipe. When the air starts, the pipe has no idea at all what’s going to happen and the sound is just trash.

It’s a signature. Few people can tell what’s going on once a pipe gets really rolling, but when it starts? “I’m pretty sure that’s the Aolian-Skinner at the National Cathedral, but don’t hold me to it. It has that odd echo in the chiff”

That doesn’t sound like a plain musical note, does it?

Have you ever tied a rope to the barn door and turned it so somebody could jump rope if they wanted to? Now turn it twice as fast and the rope breaks up into two jump ropes with a quiet part in the middle. Is the quiet part moving?

Top two illustrations.



Interesting point about the baggage.
I did not know that the first cycle carries all freqencies.
How can I test it with simple or no equipment?

Yep the quiet part is not moving, but what are you trying to say?
Would not this be the same with the actual air pressure waves?

I did not know that the first cycle carries all freqencies.

The leading edge of the first cycle carries all frequencies or at least way more than you’re expecting. That’s what gives that tick or pop when you generate tones electronically, badly.

This is the early Hammond Organ sound. It used a tone wheel to mechanically generate all the notes and just switched them on and off as needed. Each tone has that startup click.

The output from the appropriate tonewheel generator is routed as an analogue signal through the corresponding drawbar contact for each keyboard note, and then on to the associated harmonic drawbar mixer — and the audible key-click is actually generated as a by-product of this mechanical key-switching.

How can I test it with simple or no equipment?

I don’t know that you can. You can calculate it by knowing slope and rate of change of the wave. If you start a sine wave from a dead stop to operating amplitude, the starting portion of the wave has infinite slope, or infinite acceleration (or something like that) which generates the trash.

Would not this be the same with the actual air pressure waves?

Yes, exactly. The clothesline is illustrating standing waves from a badly terminated medium. My arm movement is going through the cotton rope to the garage, bouncing off and coming back. You get exactly the same effect with a bass speaker in a modern, wood floor living room.

“I want to sit here because it has the best bass.” "You don’t want to sit by the fish bowl. There’s no bass notes over there at all.

If you damped the room, covered the walls, floor and ceiling with quilts and towels, the reflections would stop, you would only have one outgoing wave and and “sweet chair” effect would vanish. The fish would get a surprise, too.

The cotton rope version of that, I suppose, would be an infinitely long trip to the garage. The wave would just not come back.

You could terminate the wave. Put springs and pistons on the rope instead of the garage and they would suck all the energy out of the rope instead of reflecting it back. No standing waves and no magic dead spot in the middle. That’s how shock absorbers on your car work.

You can terminate a room, too. You can build Helmholtz Resonators (special boxes) that eat the bass notes. I knew someone who built a recording studio like that once. Circumstances prevented him from installing full-on soundproofing.