# Sound waves

Martin McBride, 2021-07-31
Tags sound
Categories sound synthesis

Sound is created when the air around us is disturbed. This creates variations in pressure that move through the air as a sound wave. We look at what sound is in this article.

In sound synthesis, we usually work with an abstract idea of sound as a single, time varying function. For example, this graph represents a sound oscillates at 400 Hz (cycles per second) and follows a sine wave shape: This graph could represent:

• A voltage, that varies in time.
• A digital signal, that is a list of sample values stored in computer memory.
• A pure mathematical function.

Any of these representations can be converted into a real, audible sound. The time varying voltage can be fed into an amplifier and speaker to create a sound. The digital signal can be converted into a time varying voltage by computer hardware (a DAC, or digital to analogue converter), which can also be fed into an amplifier an speaker. Even a pure mathematical signal can be calculated by a computer and used to create a digital signal that can be converted to a real sound.

For the purposes of understanding sound synthesis, in this section we will just think about the mathematical function, and we will always know that it can be converted to a sound.

## Understanding the graph

The graph shows the how the sound signal varies over time.

The y-axis indicates the signal value. The signal varies between nominal values of +/- 1, with a centre value of 0. We will assume that +/- 1 is the maximum signal the system can handle. This gives the relative sound value. The actual sound depends on the amplifier and speakers you use, and the volume you set.

The x-axis represents time. In this case, the scale is milliseconds (ms). One millisecond is a thousandth of a second.

The graph shows a signal that oscillates about zero, with a frequency of 400 Hz (that is, 400 cycles per second). On cycle of teh waveform means:

• The wave starts at 0.
• It goes up to the maximum value +1.
• It goes down to the minimum value, -1.
• It returns to zero.

This is shown below, the graph shows a single cycle of the wave: Since the wave cycles 400 times a second, we expect one wave to take 0.0025 seconds, which is 2.5 ms. The graph above shows that one cycle does indeed take 2.5 ms.