# What is the relationship between decibels and intensity of sound

### Sound intensity - Wikipedia

Sound intensity level also known as acoustic intensity is defined as the power carried by sound waves per unit area in a direction perpendicular to {1}{r^{2}}}.} I(r)\propto {\frac {1}{r^{. This relationship is an inverse-square law. of a sound relative to a reference value. It is denoted LI, expressed in dB, and defined by. The sound intensities that human ears are sensitive to are very small compared some relationships between intensity ratios, pressure ratios and the standard. Loudness is typically measured in decibels, dB. where LI is the sound intensity level relative to a reference value, I is the sound's intensity.

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.

## Sound intensity

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. 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?

### Intensity and Loudness of Sound ( Read ) | Physics | CK Foundation

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. 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. This used to mean decibels of electrical power, with respect to one milliwatt, and sometimes it still does. However, it's complicated for historical reasons. When I was a boy, calculators were expensive so I used dad's old slide rule, which had the factor 0. How to convert dBV or dBm into dB of sound level? There is no simple way. It depends on how you convert the electrical power into sound power. Even if your electrical signal is connected directly to a loudspeaker, the conversion will depend on the efficiency and impedance of your loudspeaker.

And of course there may be a power amplifier, and various acoustic complications between where you measure the dBV on the mixing desk and where your ears are in the sound field. Intensity, radiation and dB How does sound level or radio signal level, etc depend on distance from the source?

A source that emits radiation equally in all directions is called isotropic. Consider an isolated source of sound, far from any reflecting surfaces — perhaps a bird singing high in the air. Imagine a sphere with radius r, centred on the source. The source outputs a total power P, continuously. This sound power spreads out and is passing through the surface of the sphere.

If the source is isotropic, the intensity I is the same everywhere on this surface, by definition.

Sound Intensity Physics Problems & Inverse Square Law Formula

The intensity I is defined as the power per unit area. So we see that, for an isotropic source, intensity is inversely proportional to the square of the distance away from the source: But intensity is proportional to the square of the sound pressure, so we could equally write: So, if we double the distance, we reduce the sound pressure by a factor of 2 and the intensity by a factor of 4: If we increase r by a factor of 10, we decrease the level by 20 dB, etc.

Be warned, however, that many sources are not isotropic, especially if the wavelength is smaller than, or of a size comparable with the source. Further, reflections are often quite important, especially if the ground is nearby, or if you are indoors. In Acoustic impedance, intensity and powerwe show how to relate RMS acoustic pressure p and intensity I: For fresh water, the specific acoustic impedance for water is 1.

So a sound wave in water with the same pressure has a much lower intensity than one in air.

For many cases in communication, isotropic radiation is wasteful: This is about the level dynamics of the amplitudes. It's often necessary to estimate how much a sound level changes. Our ears interpret a wide range of sound amplitudes, volume or loudness as change in level and change in loudness. The decibel is a very convenient unit for measuring signal levels in electronic circuits or sound pressure levels in air.

However, changes in the loudness of sounds as perceived by our ears do not conform exactly to the corresponding changes in sound pressure level. Loudness is the quality of a sound that is the primary psychological correlation of physical strength amplitude. Loudness, a subjective feeling, is often confused with objective measures of sound pressure level SPL such as decibels. Sound level or noise level is a physical quantity measured with measuring instruments.

That is not the same.

We are told by psycho-acousticians that a level 10 dB greater usually means "double the loudness" or "twice as loud". A decibel is one-tenth of a bel, which is the logarithm of the ratio of any two energy-like quantities or two field-like quantities. In the newsgroups these often misunderstood statements are explained rather less accurately.

The perceived loudness of the sound depends on several factors: A typical question on the internet: Decibel levels and perceived volume change A person feels and judges sound events by exposure time, spectral composition, temporal structure, sound level, information content and subjective mental attitude. Sometimes, even the timbre or the acoustic spectrum representing the number and relative strength of overtones is regarded as one of the parameters.

However, "timbre" can only count as a parameter in a figurative sense, because it does not consist of a variable with a discrete value.