# | wiki.naturalfrequency.com | ECOTECT COMMUNITY WIKI!

Archive site for Autodesk Ecotect Analysis educational resources, notes and tutorials

# Sound

A vibrating object will produce a sequence of compressions and rarefactions in the air surrounding it. These small fluctuations in air pressure travel away from the source at relatively high speed, gradually dying off as their energy is spread over a wider and wider area and is absorbed by the medium. What we call sound is simply the sensation produced by the ear when stimulated by these vibrations.

Consider the air close to the surface of some vibrating object. As the surface moves forwards, the air molecules next to the surface are pushed closer together to form an area of increased pressure. The air cannot move back into its original position as the space is now occupied by the advancing surface. The increased pressure forces some of this air to move outwards, which then pushes the air further out closer together and so on, creating a pressure wave moving away from the surface. As the vibrating surface recedes, it creates an area of reduced pressure, drawing the nearby air back towards it, as shown in Figure 1 below. For us to be able to perceive this as sound, these cycles have to occur many hundreds or even thousands of times a second.

Figure 1 - Slow motion simulation of a propagating sound wave in air.

### Properties of Sound

If you were to graph the pressure maxima and minima at any given instant, what you get is something that looks like a sinusoidal wave. It should be noted that air cannot sustain any form of shear stress so sound can only be transmitted as a longitudinal wave. If you are interested in experimenting with different aspects of longitudinal waves, download a free Windows program the WaveTool.

Thus the graph showing a sine wave below refers only to variations in pressure or compression, not to any actual displacement of air. From this graph, though, the wave motion of a sound can be described in terms of its Amplitude, Frequency, Velocity and Wavelength.

##### Amplitude

Refers to the difference between maximum and minimum pressure. In a sound wave, pressure fluctuations are symmetrical about the current atmospheric pressure (as measured by a barometer). For simplicity, and because this value can take hours to change, a reference value of zero is normally used. Thus maximum pressure is given as a positive value and minimum as a negative.

##### Frequency

Refers to the number of pressure peaks that pass a particular point in space over a period of one second. Thus a 1kHz (1000Hz) sound would have 1000 waves pass a point each second.

##### Wavelength

Refers to the physical distance between successive pressure maxima and is thus dependant on the speed of sound in the medium divided by the frequency of the wave. This relationship is given by:

$\large V = l * f$

Where
V = velocity (m/s),
l = wavelength (m), and
f = frequency (Hz).
##### Velocity

Refers to the speed of travel of the sound wave, basically how far a specific pressure maxima moves in one second. This varies between mediums and is also dependant on temperature. Assuming air acts as an ideal gas, its velocity relates to temperature as follows:

$\large V = 331.5 + (0.6 T)$

Where
V = velocity (m/s) and
T = air temperature (Ã‚Â°C).

In other materials, the speed of sound can vary quite substantially. The following table shows the speed of sound in a number of different materials.

Material Speed of Sound (m/s)
Steel 6100
Aluminium 4877
Brick 4176
Hardwood 3962
Glass 3962
Copper 3901
Brass 3475
Concrete 3231
Water 1433
Cork 366
Air 343
Rubber 150
Table 1 - Speed of sound in a selection of materials (from the IAC Noise Control Reference Handbook, 1989 Edition).

## An Interactive Calculator

It is important to gain some sort of feel for the relationship between all these different aspects of sound waves. This will inform you of just what sort of dimensions a sound wave can occupy. The integrated calculation tool immediately below allows you to experiment with different values for each parameter, assuming that the sound is travelling through the air, which is usually what we are interested in as building designers.

Table 2 - Calculator for the properties of sound in air. To use it, simply change any value and then use the TAB key or click the mouse in an empty area of the page to automatically update all the other values.
Properties of Sound in Air
Temperature (T): °C   Frequency (F): Hz
Velocity (V): m/s   Wavelength (l): m

Acoustic Design
Sound: Absorption