Newbie Theory - Sound Waves, Frequency

After weeks of reading all the books I have - I am still struggling with the basic theory of sound to voltage
Can somebody point me int he right direction - I am amost there ..

Part 1
In the standard sine wave graph
The Y axis is amplitude - I take this to be volume or loudness
The X axis is Cycles or Hz

One sine wave goes up and down once - this is 1 cycle and 1 hz
(am i right so far?)


Part 2
If a cycle is very fast then the note is higher..
e.g. 15,000 cycles (15khz) is screeching and 20 cycles (20hz) is bowel wrenching

Problem
How does Parts 1 and 2 relate to each other .... over time?
I am assuming that the 0 level of the Y axis of the Hz graph is common to all frequencies..
So a sine wave with a very short cycle (high note) takes up a very very small portion of the x axis, whereas a sine wave with a very long cycle takes up a very large portion of the x axis.
If the high note was louder than the low note the amplitude of the high note in the cycle would stretch up the Y axis...

By writing this I think I have just answered my riddle so I will continue...
Can somebody confirm?
So for the same time period...
If I play two notes one high and then one low each of equal duration..
I may have 30 different cycles for the high note and then a space and then 3 different cycles for the low note for the same time period...

Close...

The X axis is time. So imagine yourself moving from the origin off to the right, watching that sine wave line go up and down and simulaneously feeling the air pressure go up and down against your ear. A higher frequency would have the sine waves much narrower, a lower frequency much wider.

[quote author="uk03878"]After weeks of reading all the books I have - I am still struggling with the basic theory of sound to voltage
Can somebody point me int he right direction - I am amost there ..

Part 1
In the standard sine wave graph
The Y axis is amplitude - I take this to be volume or loudness
The X axis is Cycles or Hz

One sine wave goes up and down once - this is 1 cycle and 1 hz
(am i right so far?)

[/quote]

No. Y is amplitude, i.e voltage. But yes, this is loudness as well
X is not Hz, but time. That is, if you view a sinusoid waveform on your oscilloscope

In cases where X is frequency (or Hertz), you have a frequency-response plot. If you only had a single frequency here, you'd have a spike at that freq, nothing else.

[quote author="uk03878"]
Part 2
If a cycle is very fast then the note is higher..
e.g. 15,000 cycles (15khz) is screeching and 20 cycles (20hz) is bowel wrenching[/quote]

Yes.

Jakob E.

Thanks guys - you do not know how chuffed I feel right now
The penny is starting to drop.....
It's those blooming frequency graphs which confuse everything..

> One sine wave goes up and down once - this is 1 cycle and 1 hz

One cycle, yes.

One Hertz only if the time to complete the cycle is 1 Second.

> The X axis is Cycles or Hz

No, it is time. You make this any convenient size. Say 1 Second. Play A=440. You see 440 wiggles in one second. That is too many for clear seeing, you would change your time-width to maybe 1/100 seconds so you would see 4.4 cycles, or fine-tune to 1/220 seconds so you would see 2 complete cycles.

You ever used a tape recorder? Hold some tape over a candle to get it all sooted-up. Thread it on the tape deck and get it going constant speed, say 30 inches per second. Tie a little-teeny "pick" to one string of your guitar or bass. Pluck the string and hold it near the tape so the vibration of the string and micro-pick draw a pattern in the soot on the moving tape.

The pattern will be remarkably like the squiggles in the grooves of a phonograph record, if you have ever seen one of those. But using tape makes it easier to think about.

Say you plucked a note somewhere below A=440, which happens to be 300Hz. If you look close at the tape you will see 10 squiggles per inch. 30 inches per second times 10 cycles per inch is 300 cycles per second. Try again with the lowest note on a flat bass, about 30Hz. You will see one big squiggle per inch. Put thin strong steel string on your mini-ukelele, tune it up to 3,000Hz, and you'll get 100 wiggles per inch.

Don't play guitar? Take any acoustic source, put up an air-barrier. The barrier will vibrate with the sound. You can try to plot this on sooted-tape, though in practice acoustic pressures and mechanical motions cause by acoustic pressures are extremely small, hard to read by eye.

If you look even closer, you will see that guitar and bass don't make single pure sine waves, but a big squiggle with little squiggles added to it. These are harmonics. With math, we can break-down any possible repeating wacky-wave into combinations of pure sine waves which can be computed individually. So we often pretend audio is sine waves, at least for testing. But a pure sine wave is very dull musically.

> The Y axis is amplitude - I take this to be volume or loudness

Play soft. Wiggles are small. Play loud. Wiggles are big. Just like you see when you play guitar.

This is NOT really the same as loudness. It is the moment-by-moment position of the string. Your ear averages the instantaneous amplitudes into an impression of "loudness". Yes, big wiggles tend to be louder. But some instruments have big peaks in the plot of instantaneous position/pressure yet linger at smaller vibration locations most of each cycle. These don't sound as loud as the narrow spike of the wave suggests. Also we don't hear low tones unless they are very loud, etc.

Instead of a micro-pick on a sooty tape, rig the string's sideways vibration to a linear-slider potentiometer. Put +1V on one end, -1V on the other end. Measure the voltage on the moving wiper. You need VERY fast eyes and meter to read this: needle-meters don't waggle 400Hz and your eye can't see the wags, just the blur. But there will be a varying voltage that is exactly related to the varying position of the vibrating string. It will be a small voltage. If you invent a voltage amplifier, you can get a bigger voltage. Invent a speaker, and that amplified large voltage can make a sound much bigger then the guitar alone, yet exactly the same. (Well, never exactly, but we get better every century.)

Nice explanation and experiment PRR. I would love to see more of this sort of thing.


Can I buy a Guiness or a Sam Addams?
:guinness: :sam:


:wink:
Patina

wooah - many thanks PRR

Can we come back to the harmonics thing then please....

So if I play a low note and at the same time a harmonic is generated (either artifically or via the instrument) - that is twice the frequency AND the same amplitude..

I will see the combination of the results of two sine waves superimposed on one another (one of one cycle and the other of two cycles for the same time period)
I have just drawn it and it looks like a steep rise - a ripple (looking like a "m" - then a steep dip below the 0 point on the Y axis then back up sharply to the 0 point.

One more point - that is going to be the next point - I still can't get my head around the "sine wave" going beneath the 0 point on the Y axis...
Negative amplitude - sorry it hasn't clicked....

[quote author="uk03878"]
So if I play a low note and at the same time a harmonic is generated (either artifically or via the instrument) - that is twice the frequency AND the same amplitude..
......
One more point - that is going to be the next point - I still can't get my head around the "sine wave" going beneath the 0 point on the Y axis...
Negative amplitude - sorry it hasn't clicked....[/quote]


Twice the freq but not necessarily the same ampliude.



Negative amplitude is simply 'amplitude in the opposite direction' (or phase). So think about looking at a guitar string at rest and then plucking it. First it moves one way (positive), then back past it's original position (zero), then away from the rest position in the other direction - that's negative.