Basic Acoustics

What is sound?

Sound is a form of energy. Other types of energy are for example heat, light, and electromagnetism.

Sound waves are generated by the movements of molecules in mediums such as air or water. Energy entering a medium will move the molecules from their resting position and create pressure differences that result in sound waves.

The sound wave is the propagation of the pressure differences. Molecules are not moving away in a single direction, they are only moving back and forth. When the air pressure goes back to normal again, the molecules go back to their resting position.

The more the energy, the bigger the air-pressure change and the louder the sound measured in decibels. The longer the wavelength, the lower frequency the sound has, and visa-versa.

Frequency

The frequency of a sound is defined as the number of oscillations (completed cycles) per second, measured in Hertz (Hz). For example, if a sound wave makes 1000 oscillations per second, we have a tone of 1000 Hz.

The normal frequency range of human hearing is 20 to 20000 Hz. However, we all start losing the highest frequencies when we are quite young due to the effects of aging. Adult will normally have an upper hearing limit of 15000 to 18000 Hz.

The most common frequencies emitted when people speak are in the frequency range of 500 to 2000 Hz.

A low frequency sound (i.e. a low number oscillations per second) could, for example, be the sound of thunder. The sharpening of a knife could be an example of a high frequency sound with many oscillations per second.

Velocity of sound waves in different media

Sound velocity, or speed of sound waves in different media, varies a lot. It goes much faster in more solid media. The most well-known velocity is 340 meters per second (m/s), which is the speed of sound in normal air.

Other common velocities of sound in different media are provided in the table below.

The relationship between velocity, wavelength and frequency is as follows:

Velocity = wavelength x frequency

In air at normal temperature and at sea level, the wavelength can be calculated as follows:.

From the formula, you can see that changing the velocity will change the wavelength.

 

Sound pressure level

When we measure the strength of a sound, we are measuring the sound pressure variations which are measured in Newtons per square meter (N/m2). The unit is decibel (dB).

The threshold of hearing is the lowest sound we can hear as human beings. Our threshold is 0,00002 N/m2 at 1000 Hz.

This threshold value is used as a reference level in the calculation of the sound pressure level (Lp), expressed in decibel (dB).

Converted into sound pressure level (Lp), this threshold corresponds to 0 decibel (dB).

The pain threshold is when the sound starts to hurt in our ears. The sound pressure variations are then about 20 N/m2.

Calculated into sound pressure level (Lp) this corresponds to 120 decibel (dB).

The threshold of pain: 20 N/m2.

This is how you calculate the dB level: The measured sound pressure for the actual sound, p N/m2, squared and divided by the sound pressure at the threshold of hearing, p0 (0,00002 N/m2) squared.

The logarithm of this quotient is multiplied by 10 and you have the dB value.

p = the measured sound pressure for the actual sound, p N/m2p0 = the sound pressure at the threshold of hearing.

Due to the logarithmic nature of auditory perception, you cannot think of sound pressure levels in linear terms.

In the picture you can see that adding two sources with equal dB only increases the overall sound pressure level by 3 dB. Even though the energy has doubled, we do not experience the sound as twice as loud.

If you add 10 equal sources, you end up with an increase of 10 dB. You can also see to the right the relative changes of sound energy. 10 dB corresponds to a doubling of loudness for human listeners.

What is a tone?

Pure tone = A pure tone consists only of a single frequency. It can be generated by electronic instruments and devices. It has a sinusoidal wave form, which is a repeating pattern. This gives it a clear sound to the human ear.

Complex tone = A complex tone is the sum of two or more pure tones and its waveform has an underlying pattern that repeats. The underlying frequencies that make up a complex tone have different names. The lowest frequency is called the fundamental, and is typically heard more loudly than the other tones. The remaining higher frequencies are called overtones.  Complex tones are generated by musical instruments, human voices and many naturally occurring phenomena. They are perceived as more interesting to listen to than pure tones, and sound more or less beautiful depending on the physical properties of the resonating body that produces them.

What about all the noise that we have around us? Are they pure tones or complex tones? Noise is defined as being any sound that is “unwanted”. So it can be either type of tone, or both happening simultaneously. It can also be a sound with no repeating pattern, the auditory equivalent of chaos. In the picture below, you can see the waveform of “white noise”, which sounds like static. Many types of electrical equipment produce noise like this, such as ventilation systems and projectors.

In the figure you can see how sensitive our ears are at different frequencies. You can also see the ranges of types of sound – from music and speech. Any sound occurring within these ranges could be noise or nice, depending on the context in which it is heard and the activities that are happening at the time.

Weighting curves – for instrument measured sound levels

dB(A) vs. dB(C)

Different kinds of filters are often used when we measure dB. These filters have different sensitivity to different frequencies.

A-filter

The A-weighted decibel filter (dBA) attenuates the lower frequencies , making this weighting correspond more closely to how the human ear perceives sound.

An A-weighted sound pressure level of 75 dB is written LpA = 75 dB.

C-filter

The C decibel weighting (dBC) takes more of the low frequencies into account. This is for example often used when measuring the sound pressure levels in concerts.

Sound absorption

Sound absorption is distinct from sound insulation. Absorption takes place  within a room, while insulation occurs when the sound transmission between rooms is reduced.

Definition of sound absorption coefficient:

When a sound wave strikes one of the surfaces of a room, some of the sound energy is reflected into the room and some energy penetrates the surfaces.

Some of the sound energy is absorbed by conversion to heat energy within the material, while the rest is transmitted through to the other side.

The level of energy converted into heat energy depends on the sound-absorbing properties of the material.

A material’s sound-absorbing properties are expressed by the sound absorption coefficient, α, (alpha), which is expressed as a function of the frequency of the sound.

α ranges from 0 (total reflection) to 1.00 (total absorption).

Sound insulation vs. absorption

Sound insulation is about the ability of a dividing construction to reduce the amount of sound being transmitted through the construction (see picture). This means it is in principle the difference in sound levels in two adjacent spaces. Sound insulation must be clearly separated from sound absorption; these are two very different phenomena. Sound absorption takes place within a room, while insulation occurs between rooms.

Room-to-room insulation

In many cases, a continuous suspended ceiling is chosen to achieve maximum flexibility. However, these constructions will give lower sound insulation unless the partitions are allowed to penetrate the suspended ceiling or reach up to the soffit.

If partitions do not reach the structural soffit, a horizontal transmission path for the sound via the gap above the suspended ceiling is created. Therefore, traditional acoustic ceilings often provide insufficient sound insulation. In these cases, special acoustic ceiling systems are required which offer additional sound insulating properties.

When estimating the airborne sound insulation:

  • Consider the whole structure
  • Note that on-site values are lower than laboratory values
  • Laboratory value/site value

In practice on site, the room-to-room sound insulation (R′w) can be estimated to be 5-8 dB lower than the lowest value in laboratory for the suspended ceiling and partition respectively. This is due to the fact that interaction between the suspended ceiling and the partition considerably reduces sound insulation. Also flanking transmission might occur and some installation details might not be perfect.

 

Recommendations

In order to provide reasonable privacy, we recommend that normal offices have sound insulation between adjacent rooms of R′w = 35 dB. This requires a suspended ceiling with a laboratory value Dn,f,w ≤ 40 dB.

 

The general approach is to combine a sound insulating suspended ceiling with partitions that offer at least the same sound insulation value in a laboratory. Other transmission paths, i.e. ventilation systems, should have an even better sound insulation value. The values used for the suspended ceiling and the partition should also include possible installations into them, such as lighting and ventilation units or doors and windows. It’s crucial to prevent leakage due to, for example, incomplete sealed junctions between separating wall and flanking surfaces, continuous cable tray, or openings around different construction details.

 

Acoustics glossary

https://www.ecophon.com/en/about-ecophon/acoustic-knowledge/acoustics-glossary/