Amplitude
Amplitude is a crucial concept that describes the strength or intensity of a sound wave.
What is Amplitude?
Amplitude refers to the maximum displacement of a sound wave from its resting position (or centreline). In other words, it is the height of the wave’s peaks or the depth of it’s troughs. The greater the amplitude, the louder the sound.
Measuring Amplitude:
There are several ways to measure the amplitude of a sound wave:
Peak amplitude: This is the maximum positive or negative displacement of the wave from it’s centreline. It is the highest point the wave reaches in either direction.
Peak-to-Peak Amplitude: This is the total distance between the positive and negative peaks of the wave. It is essentially twice the peak amplitude.
Root Mean Square (RMS) Amplitude: This is a way to calculate the average amplitude of a wave over time. It is a more accurate representation of how our ears perceive sound intensity. To calculate RMS amplitude, you square the amplitude values at various points along the wave, find the average of those squares, and then take the square root of that average.
The Relationship between Peak and RMS Amplitude:
For a perfect sine wave (a pure tone), the RMS amplitude is always about 0.707 times the peak amplitude. Conversely, the peak amplitude is about 1.414 times the RMS amplitude. This relationship can be expressed with the following formulas:
RMS Amplitude = 0.707 x Peak Amplitude
Peak Amplitude = 1.414 x RMS Amplitude
Diagram of a wave showing peak, peak-to-peak, and RMS amplitude.
Amplitude and Sound Intensity:
The amplitude of a sound wave is directly related to its intensity, which is the amount of energy it carries. Doubling the amplitude of a wave increases its intensity by a factor of four. This means that a sound with twice the amplitude will be perceived as being four times as loud.
Formula:
Intensity ∝ Amplitude^2
Or more precisely: Intensity = (Pressure Amplitude)^2 / (ρ × c)
Where: ρ = density of the medium (e.g., air)
c = speed of sound in the medium
Explanation:
Intensity is a measure of the energy carried by the sound wave per unit of area, and is directly related to how loud we perceive the sound to be. The first equation, “Intensity ∝ Amplitude^2”, is a simplified way of expressing this relationship.
The “∝” symbol means “is proportional to”. So, this equation states that the sound of a wave is proportional to the square of its amplitude. In other words, if you double the amplitude of a sound wave, the intensity will increase by a factor of four (2^2 = 4).
The second equation provides a more precise mathematical definition of this relationship:
Intensity = (Pressure Amplitude)^2 / (ρ × c)
Where:
Pressure Amplitude is the maximum change in pressure caused by the sound wave (which is directly related to the amplitude of the wave).
ρ (rho) is the density of the medium through which the sound wave is traveling (e.g. air)
c is the speed of sound in that medium.
Let's break this equation down:
The pressure amplitude is squared because the energy of a wave is proportional to the square of its amplitude. This is true for many types of waves, including sound waves and electromagnetic waves.
The density (ρ) and speed of sound (c) in the medium are important because they determine how much energy is needed to create a given pressure change. In denser media or media with a higher speed of sound, more energy is required to create the same pressure change.
Dividing by (ρ × c) normalizes the intensity so that it represents the energy per unit area. This allows us to compare the intensities of sounds in different media.
In summary, this equation shows that the intensity of a sound wave depends on both its amplitude and the properties of the medium it's traveling through. The intensity increases with the square of the amplitude, but it is inversely proportional to the density and speed of sound in the medium.
Understanding this relationship is important in audio engineering because it helps us predict how loud a sound will be based on its amplitude and the environment it's in. It also helps us understand how to control the intensity of sound waves by adjusting their amplitudes or changing the properties of the medium they're traveling through.
