Amplitude

The amplitude of a periodic variable is a measure of how much it changes over one full cycle, such as over time or space. It tells us how far the variable goes from its middle value to its highest or lowest point. For example, when you watch a swing move back and forth, the amplitude is how far the swing goes from the center to its farthest point.

There are different ways to define amplitude, but they all depend on the size of the differences between the highest and lowest values the variable reaches. In some older books, people sometimes used the word "amplitude" to mean something else called the phase of a repeating motion, but today we usually keep these ideas separate.

Amplitude is important in many areas of science and engineering because it helps us understand how big or strong waves and vibrations are, whether we're looking at sound waves, light waves, or waves on a string.

Definitions

In science and engineering, amplitude is a way to measure how big a wave or signal gets. It tells us how much the signal moves above and below a normal level.

There are a few ways to measure amplitude. Peak amplitude is the highest point the signal reaches. Peak-to-peak amplitude is the total distance between the highest and lowest points. Semi-amplitude is half of the peak-to-peak amplitude, often used in astronomy to study stars and planets. Root mean square (RMS) amplitude is used in electricity to measure how much power a signal can deliver, especially for alternating currents. Each type of amplitude helps scientists and engineers understand different aspects of waves and signals.

Formal representation

In the simple wave equation, the symbol A represents the amplitude. This tells us how far the wave goes above or below its middle point. The equation shows how a variable x changes over time, with ω representing how fast the wave oscillates, and t standing for time. The constants K and b adjust the wave’s start time and position.

Units

The units used to measure amplitude depend on the type of wave. For waves on a string or in water, amplitude is measured as a displacement. When talking about sound waves, amplitude relates to changes in air pressure, which affects how loud a sound is.

For electromagnetic radiation, such as light, the amplitude relates to changes in the electric field of the wave. This concept is important for understanding how signals like radio waves work.

Amplitude envelopes

Amplitude envelope describes how the loudness of a sound changes over time. A steady tone has the same loudness throughout, like a flat note on a piano. But many sounds, like clinking glasses or hitting a drum, start loud and quickly quiet down. These sounds have what we call percussive amplitude envelopes.

Percussive amplitude envelopes help us understand sounds that begin suddenly and then fade out. They include a quick loud start, a decay in loudness, a middle part where the sound stays at a certain level, and finally a release where the sound ends.

Amplitude normalization

When dealing with complex sounds that have many overtones, we can give each overtone its own special pattern of loudness changes over time. However, this can also change how loud the overall sound seems. To avoid this, we can adjust the loudness of each overtone so that together they always add up to the same total — like making sure all the pieces of a puzzle fit perfectly.

This helps us control the loudness of the sound separately from its tone quality. In sound recognition, we can also use the highest loudness point to help match similar sounds, making it easier to tell if two sounds have the same tone even if one is louder than the other.