Vehicle Acoustics Basics

1.0 Speed of Sound and Light

In air, sound propagation is slower than that of light.
One notices this very clearly during thunderstorms

1.1 Propagation of Sound in Air

An acoustic wave propagates by small pressure changes that are transmitted locally through the medium, e.g. air.
The propagation speed of these waves is called the speed of sound. For air at room temperature the speed of sound is 340 m/s.
This value must not be confused with the speed of the particles in the medium: only the pressure fluctuations (or acoustic pressure) propagate.
In fact, the molecules of the medium keep, on average, the same position when oscillating around their equilibrium position (i.e. small pressure fluctuations).
After a sound wave has passed, the molecules return to their initial position.

1.2 Emission, Propagation & Reception

Emission is the mechanism by which a sound source causes an oscillatory movement in the ambient medium.
Propagation is the phenomenon by which this movement is transmitted through the medium.
Reception is the phenomenon by which sound is detected. Such a device could be, for example, a microphone or a human ear.
In applied acoustics, one is interested in these 3 phenomena for:
– reducing noise at source
– modifying a propagation path
– measuring noise

1.3 Airborne versus Structureborne Sound Transmission

Airborne sound is transmitted via fluids (gases & liquids) and can be perceived with the human ears

Structureborne sound or vibrations are transmitted in solids and can be perceived with the human body

2 Acoustic Quantities

Sound pressure (p): is what the ear detects as noise. Units are Pa or N/m2

Sound power (P): the amount of noise emitted from a source:

Sound Intensity (I): the sound intensity of a sound wave describes the direction and net flow of acoustic energy through an area.

Intensity is also the time-averaged rate of energy flow per unit area. If the energy is flowing back and forth resulting in zero net energy flow then there will be zero
intensity:

Free field:

refers to an idealized situation where the sound flows directly out from the source and both pressure & intensity drop with increasing distance according to the inverse square law.

2.1 Acoustic Quantities

Diffuse field: in a diffuse field the sound is reflected many times such that the net intensity can be zero. E.g. reverberant room.

Particle velocity: pressure variations give rise to Movements of the air particles. It is the results of Pressure and particle velocity that results in the Intensity:

Acoustic impedance:
Is defined as the product of the mass density of a medium and the velocity of sound in that medium:

2.2 Acoustic Quantities

Reference conditions:

Sound power level:

Particle velocity level:

Sound pressure
p0 = 20uPa:

Sound intensity
I0=1pW:

2.3 Sound Pressure Level & Decibel

The decibel (dB) is a logarithmic unit which is used in science to compare the quantity of interest with a reference value, often the smallest likely value of the quantity.

Sometimes it can be an approximate average value.
In acoustics the decibel is most often used to compare sound pressure with a reference pressure.

The reference sound pressure (in air) = 0.00002 = 2E-5 Pa (rms)
Acousticians use the dB scale for the following reasons:

Quantities of interest (e.g. sound pressure) often exhibit such huge ranges of variation that a dB scale is more convenient than a linear scale.
The human ear interprets loudness more easily interpreted with a logarithmic scale than with a linear scale.

The sound pressure level (SPL) indicates the sound pressure, p, as a level referenced to 0.00002 Pa, calibrated on a decibel scale

3. Calculation of Overall Level

4 sources (or windows) with 90dB sound intensity each will sum up to 96dB overall !

3.1 Calculation of Overall Level

3 sources (or windows) with 90dB sound intensity and one source with 60dB will sum up to 94.7dB overall !

3.2 Calculation of Overall Level

2 sources (or windows) with 90dB sound intensity and two sources with 60dB will sum up to 93dB overall !

3.3 Calculation of Overall Level

1 source (or windows) with 90dB sound intensity and three sources with 60dB will sum up to 90dB overall !

4. Frequency

Any motion that is repeated is called a periodic motion. Examples of periodic motions are the earth’s rotation, a beating heart, the wings of a hummingbird and the vibration of a music instrument’s string.
A period is the time required for one complete cycle. The frequency is the number of cycles occurring in a given time period.
Thus the frequency is the inverse of the period:

The units used in the past (cycles per seconds = cps) are nowadays more commonly expressed in Hertz (Hz) => 1 cps = 1 Hz

Motion	Period (sec)	Frequency (Hz)
Earth’s rotation	24x60x60 = 86400	0,0000115
Heart beat	1	1
Hummingbird’s wings	0.016	62.5
Concert A	0.0022727	440

4.1 Wavelength, Pure + Harmonic Sounds

It can be shown that a sound that has a time periodicity, is also periodic in space. The time period T corresponds to the wavelength in the direction of propagation.

The length of the wave (or wavelength) is one of the most important parameters in Applied Acoustics and must be taken into account for many applications. Our character shown opposite is 1.7m high and this corresponds to the wavelength at the frequency of f = 200 Hz – using a speed of sound of c=340 m / s.

4.2 Random Sounds

Real sound waveforms are not as simple as that of pure tones and harmonic sounds.

Very often, no repetitive pattern can be identified in a signal.

One cannot predict the signal behavior from its time history:

It has a random waveform.

Such random sounds are called “noises” because they are often more disturbing than periodic or almost periodic sounds.

The audio recordings below allow you to experience the complexity of such time histories.

5. Octave Bands

Complete (1/1) octave bands represent frequency bands where the center frequency of one band is approximately twice that of the previous one:

5.1 Frequency Weighting

The human ear has nonlinear, frequency dependent characteristics, which means that the sensation of loudness cannot be perfectly described by the sound pressure level.

To derive an experienced loudness level from the SPL, the spectrum is multiplied by a weighting function.

A number of equal loudness contours are shown below:

5.2 Frequency Weighting: A,B & C

A-weighting modifies the frequency response such that it follows approximately the equal loudness curve of 40 phons.
The A-weighted sound level has been shown to correlate well with subjective responses.
The B and C-weighting follow more or less the 70 and 100 phon contours: