Understanding waveform representation?

I am new to audio things and I have trouble understand the waveform representation, e.g. in Audacity the y-axis goes from -1 up to +1 (please see screenshot below). What does this mean? What does the y Axis represent at all? I think it should be the loudness, but how can the loudness be negative? And don't I need multiple values at the same time on the y axis for different frequencies? Or do audio files only contain one value for a given time? I am just confused because on a spectogram one has multiple points for one point in time, on the waveform one has only one point... I already googled, but couldn't find an explanation. And help, including literature recommendations, are welcome. Thank you very much!

(I also checked the Audacity documentations on this, but it didn't help me!)

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Sound is a series of negative and positive energy. Technically the Y - Axis does represent "loudness" though loudness can be measured in many different ways. A full positive to negative change is known as a "cycle". Faster cycles means higher pitches, slower cycles means lower pitches. You can simulate this by dragging an object over a textured surface, the faster you drag, the higher the pitch. Alternatively, you could also just blow air through your mouth (whistling).

Its easier to think of the waveform as the "base" data. A spectrogram plots the frequencies generated from that waveform over time.

Also low and high pitches can play at the same time, it will look like the higher pitched sound is "riding" on top of the lower pitched sound in the waveform. The waveform is still a single value.

From that one point of the waveform we can generate a spectrum of all frequencies at that given time. We can then keep grabbing points over time to form a graph of frequencies over time, or a spectrogram.

A spectrum, spectrogram are just different ways to graphically represent sound.

• Thank you very much for that detailed answer william, I have some follow up questions: 1) Imagine there are two frequencies in a room. Now recording the sound, I guess I record one frequency, therefore the combined one of both? 2) I don't understand how I can get from a waveform to a spectogram. Do you have any link explaining this? Thank you very much! – stefan.at.wpf May 20 '12 at 10:32
• -1 Sorry, there's just too much wrong information in here. — "Negative and positive energy"?? — Loudness can certainly be represented in many different ways, but points in a waveform don't do that. — A cycle is always at least negative-to-positive-to-negative, though it can also be 0-to-0-to-0 or more complicated. —— Otherwise, you've got some good points here, clarify the answer a bit and I'll upvote. – leftaroundabout May 21 '12 at 0:33
• I agree leftaroundabout. -1 for william. +1 for leftaroundabout. – DoktorHauser Jun 25 '12 at 10:41

Imagine a swimming pool with no ripples. Then drop a pebble in. Ripples will move out from that point. If you choose a point to measure the height you will see it moves up and down from its rest point. Drop another pebble somewhere else and the ripples will interfere, adding and subtracting from each other. The waveform will look complex but the height at your measurement point will still just be one number.

Instead of dropping pebbles, imagine vibrating paddles on the surface of the water at different speeds. This will give you a very chaotic looking waveform, but Fourier transforms (a branch of mathematics) you can take that waveform and derive the frequencies of the vibrations.