# Decibels and intensity relationship

### Intensity and the Decibel Scale

Intensity of sound and how it relates to loudness, the decibel levels of different sounds and Relationship between decibel level and intensity. The human ear can detect sound of very low intensity. On the decibel scale, doubling the intensity corresponds to an increase of 3 dB. We get this thing again — the intensity-pressure amplitude relationship. . By convention, sound has a level of 0 dB at a pressure intensity of 20 μPa and.

## Intensity and the Decibel Scale

Since energy is conserved and the area through which this energy is transported is increasing, the intensity being a quantity that is measured on a per area basis must decrease. The mathematical relationship between intensity and distance is sometimes referred to as an inverse square relationship. The intensity varies inversely with the square of the distance from the source. So if the distance from the source is doubled increased by a factor of 2then the intensity is quartered decreased by a factor of 4.

Similarly, if the distance from the source is quadrupled, then the intensity is decreased by a factor of Applied to the diagram at the right, the intensity at point B is one-fourth the intensity as point A and the intensity at point C is one-sixteenth the intensity at point A. Since the intensity-distance relationship is an inverse relationship, an increase in one quantity corresponds to a decrease in the other quantity.

The velocity and acceleration changes caused by a sound wave are equally hard to measure in the particles that make up the medium. Density fluctuations are minuscule and short lived. The period of a sound wave is typically measured in milliseconds. There are some optical techniques that make it possible to image the intense compressions are rarefactions associated with shock waves in air, but these are not the kinds of sounds we deal with in our everyday lives.

Pressure fluctuations caused by sound waves are much easier to measure. Animals including humans have been doing it for several hundred million years with devices called ears.

Humans have also been doing it electromechanically for about a hundred years with devices called microphones. All types of amplitudes are equally valid for describing sound waves mathematically, but pressure amplitudes are the one we humans have the closest connection to.

In any case, the results of such measurements are rarely ever reported. Instead, amplitude measurements are almost always used as the raw data in some computation. So, when it is used to give the sound level for a single sound rather than a ratio, a reference level must be chosen.

This is very low: Nevertheless, this is about the limit of sensitivity of the human ear, in its most sensitive range of frequency. Usually this sensitivity is only found in rather young people or in people who have not been exposed to loud music or other loud noises.

Personal music systems with in-ear speakers are capable of very high sound levels in the ear, and are believed by some to be responsible for much of the hearing loss in young adults in developed countries. Divide both sides by What does 0 dB mean?

This level occurs when the measured intensity is equal to the reference level. This is a small pressure, but not zero. It is also possible to have negative sound levels: Not all sound pressures are equally loud. This is because the human ear does not respond equally to all frequencies: For this reason, sound meters are usually fitted with a filter whose response to frequency is a bit like that of the human ear.

More about these filters below. Sound pressure level on the dBA scale is easy to measure and is therefore widely used. It is still different from loudness, however, because the filter does not respond in quite the same way as the ear.

To determine the loudness of a sound, one needs to consult some curves representing the frequency response of the human ear, given below. Alternatively, you can measure your own hearing response. Logarithmic measures Why do we use decibels? The ear is capable of hearing a very large range of sounds: To deal with such a range, logarithmic units are useful: Logarithmic measures are also useful when a sound briefly increases or decreases exponentially over time.

This happens in many applications involving proportional gain or proportional loss. Using this filter, the sound level meter is thus less sensitive to very high and very low frequencies.

Measurements made on this scale are expressed as dBA. The C scale is practically linear over several octaves and is thus suitable for subjective measurements only for very high sound levels.

Measurements made on this scale are expressed as dB C. There is also a rarely used B weighting scale, intermediate between A and C. The figure below shows the response of the A filter left and C filter, with gains in dB given with respect to 1 kHz. For an introduction to filters, see RC filters, integrators and differentiators.

On the music acoustics and speech acoustics sites, we plot the sound spectra in dB. The reason for this common practice is that the range of measured sound pressures is large. It thus gives large values for sounds and infrasounds that cannot readily be heard.

### dB: What is a decibel?

To convert from dB to phons, you need a graph of such results. Such a graph depends on sound level: This graph, courtesy of Lindoslandshows the data from the International Standards Organisation for curves of equal loudness determined experimentally.

Plots of equal loudness as a function of frequency are often generically called Fletcher-Munson curves after the original work by Fletcher, H. You can make your own curves using our hearing response site. The sone is derived from psychophysical measurements which involved volunteers adjusting sounds until they judge them to be twice as loud. This allows one to relate perceived loudness to phons. So that approximation is used in the definition of the phon: This relation implies that loudness and intensity are related by a power law: Wouldn't it be great to be able to convert from dB which can be measured by an instrument to sones which approximate loudness as perceived by people?

This is usually done using tables that you can find in acoustics handbooks. However, if you don't mind a rather crude approximation, you can say that the A weighting curve approximates the human frequency response at low to moderate sound levels, so dB A is very roughly the same as phons.

Then one can use the logarithmic relation between sones and phons described above.

### Intensity – The Physics Hypertextbook

Recording level and decibels Meters measuring recording or output level on audio electronic gear mixing consoles etc are almost always recording the AC rms voltage see links to find out about AC and rms. So what is the reference voltage? The obvious level to choose is one volt rms, and in this case the level is written as dBV.

This is rational, and also convenient with modern analog-digital cards whose maximum range is often about one volt rms.

So one has to remember to the keep the level in negative dBV less than one volt to avoid clipping the peaks of the signal, but not too negative so your signal is still much bigger than the background noise. Sometimes you will see dBm.