# Sound Theory

The sensation of sound is a result of vibrations in the air caused by pressure fluctuations, which can be measured with a sound level meter. Vibrations are more commonly associated with mechanical systems, but air also has mass and stiffness, and as sound travels in the air it is locally compressed and expanded. The simplest type of vibration is a pure tone, which is a one-dimensional sinusoidal vibration with only one frequency component. These sinusoidal vibrations are called simple harmonic vibrations.

Measuring sound is done with a sound level meter and can be presented by both sound pressure, measured in Pascal (Pa), and sound intensity, measured in Watt/m2.

## Amplitude

The amplitude of a periodic variable is defined as the maximum difference of the variable's extreme values over one single period, usually the distance between the top and the bottom of the curve. A large amplitude signifies high sound levels (noise) and a low amplitude signifies low sound levels (quiet). The sound wavelength is not altered when changing the amplitude, it only increases or decreases the loudness of the sound.

## Frequency

The measurement unit of frequency is Hertz (Hz), and describes the number of cycles the period is repeated per second (1 Hz = 1 cycle per second). In sound theory the most used frequencies are 20Hz to 20 000 Hz (20kHz), which is the range where the human ear can respond. However, the field of acoustics also includes ultrasonic frequencies above 20kHz, and infrasonic frequencies below 20Hz.

The sound wavelength depends on the phase velocity and frequency, and frequency is further defined by the period. The period is measured in seconds and defined as the time it takes to repeat one cycle. In other words, the wavelength characterizes the distance it takes to repeat one cycle.
Typical low frequency sound has long wavelengths and contains high levels of energy, while high frequency sound has short wavelengths and contain low levels of energy. Typical low frequency sound is represented by the bass levels and high frequency sound is usually the high pitched details.

## The Human Ear

The human ear can respond to frequencies from 20Hz to 20kHz, but has a peak of sensitivity around 3-4kHz. This is due to the resonance of the ear cavity that amplifies certain frequencies. Many years of evolution has taught the ear to be more sensitive around the frequency spectre of speech, because that is the main source of communication between humans. Therefore the ear is not equally sensitive at all frequencies.

The measuring unit for sound is Decibel (dB), and is a logarithmic unit used to express power or intensity. The human ear can hear from 0dB to 120dB, the last being the threshold of pain. A level of 120dB or higher can be dangerous for the ear, and in worst cases contribute to permanent reduced hearing.

Because of the ear's response to different frequencies, several " sound filters" have been introduced in the field of acoustics. The most common one is the A-weighted filter, which is directly based upon the loudness perceived by the human ear. This means that the sound is filtered by damping the low frequency sound because the ear is less sensitive at low audio frequencies. Additionally there exists B-, C-, D- and Z-weighted filter as well. The ones which are mostly used is C-weighted and Z-weighted filters. C-weighting includes more of the low frequency sound than A-weighting, while Z-weighting is a linear flat filter.

## Noise

Another type of sound is noise, which normally is undesired. The definition of noise is highly subjective, due to people reacting differently to what noise is. One may characterize noise from being casually disturbing to health damaging. Being exposed to high noise levels on a daily basis can reduce your hearing if no precautions are taken. If the ear has been critically damaged, there is little chance it will heal to its original state, once the ear has been injured there is no going back. Even though the definition of noise is very individual, acoustic engineers have a more objective way of characterizing it by using sound level meters.

## Examples

### Wavelength:

The equation for the wavelength is defined as: λ = c/f
Where c is the phase speed (dependent on temperature and medium) and f is the frequency.

• At 20oC in air, with f=63Hz: λ = 5.4 meters.
• At 20oC in air, with f=20 000Hz: λ = 17.2 centimeters.

### Decibel:

Converting between sound pressure level and sound intensity levels is easy, given this equation:

Where SPL is the sound pressure level in dB and SIL is the sound intensity level, the reference values are Pref = 20μ Pa and Iref = 10-12 W/m2.
Therefore, if you have measured an intensity of Irms = 10-8 W/m2 and want to find the value in decibel: