In some situations, such as tape recording, a given intensity level is assigned 0 dB, and other levels are measured in negative decibels in comparison to it. The term became accepted in the s and since then noise measurement has generally come to rely on the decibel scale and others derived from it. The PHON scale attempts to account for the subjective response of the ear to loudness, which is not possible with the decibel measurement of intensity. Appendix D gives a conversion chart of voltage and power ratios to decibels.
The formula is a little different than what is in the text, but the both give the same numbers. Since sound pressure is relative, if your pr is larger than your p, you will get negative values. You might see negative numbers on some audio equipment, that is using the loudest sound as the pr so all the volume settings are that loud a dB of 0 or less.
We will use this way of doing decibels in this illustration. In this illustration, to help you experience decibels and get a feel for how they relate to sound pressure level, you can try different decebel steps and here how the loudness changes. To see the illustration in full screen, which is recommended, press the Full Screen button, which appears at the top of the page.
Below is a list of the ways that you can alter the illustration. The settings include the following:. Play : start a series of tones starting from the loudest and decreasing in constant decibel steps.
Decibel Step Size : the series will decrease by the decibel step selected here. In the acoustic cases given above, we saw that the pressure ratio, expressed in dB, was the same as the power ratio: that was the reason for the factor 20 when defining dB for pressure. It is worth noting that, in the voltage gain example, the power gain of the ampifier is unlikely to equal the voltage gain, which is defined by the convention used here.
The power is proportional to the square of the voltage in a given resistor. However, the input and output impedances of amplifiers are often quite different.
For instance, a buffer amplifier or emitter follower has a voltage gain of about 1, but a large current gain. Different countries and provinces obviously have different laws concerning noise exposure at work, which are enforced with differing enthusiasm. Many such regulations have a limit for exposure to continuous noise of 85 dB A , for an 8 hour shift.
For each 3 dB increase, the allowed exposure is halved. So, if you work in a nightclub where amplified music produces dB A near your ears, the allowed exposure is 15 minutes. There is a limit for impulse noise like firearms or tools that use explosive shots. There are many documents providing advice on how to reduce noise exposure at the source ie turn the music level down , between the source and the ear ie move away from the loudspeakers at a concert and at the ear ie wear ear plugs or industrial hearing protectors.
Noise management and protection of hearing at work is the code of practice in the state of New South Wales, Australia the author's address. Sound pressure, sound level and dB. Sound is usually measured with microphones and they respond proportionally to the sound pressure, p. Now the power in a sound wave, all else equal, goes as the square of the pressure.
Similarly, electrical power in a resistor goes as the square of the voltage. The log of x 2 is just 2 log x, so this introduces a factor of 2 when we convert pressure ratios to decibels. Note, too, that a doubling of the power does not make a huge difference to the loudness. We'll discuss this further below, but it's a useful thing to remember when choosing sound reproduction equipment.
How big is a decibel? In the next series, successive samples are reduced by just one decibel. What if the difference is less than a decibel? Sound levels are rarely given with decimal places. The reason is that sound levels that differ by less than 1 dB are hard to distinguish, as the next example shows.
This makes the dB a convenient size unit. Standard reference levels 'absolute' sound level We said above that the decibel is a ratio.
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: it is 2 ten billionths of an atmosphere. Nevertheless, this is about the limit of sensitivity of the human ear, in its 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 some countries. So 0 dB does not mean no sound , it means a sound level where the sound pressure is equal to that of the reference level.
This is a small pressure, but not zero. It is also possible to have negative sound levels: - 20 dB would mean a sound with pressure 10 times smaller than the reference pressure, i. Logarithmic measures Why do we use decibels? The ear is capable of hearing a very large range of sounds: the ratio of the sound pressure that causes permanent damage from short exposure to the limit that undamaged ears can hear is more than a million.
To deal with such a range, logarithmic units are useful: the log of a million is 6, so this ratio represents a difference of dB. Hearing is not inherently logarithmic in response. 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. The filters used for dBA and dB C The most widely used sound level filter is the A scale, which roughly corresponds roughly to the inverse of the 40 dB at 1 kHz equal-loudness curve.
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 varies little over several octaves and is thus suitable for subjective measurements only for moderate to 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. ISO Loudness, phons and sones, hearing response curves The phon is a unit that is related to dB by the psychophysically measured frequency response of the ear.
At 1 kHz, readings in phons and dB are, by definition, the same. For all other frequencies, the phon scale is determined by the results of experiments in which volunteers were asked to adjust the loudness of a signal at a given frequency until they judged its loudness to equal that of a 1 kHz signal. To convert from dB to phons, you need a graph of such results.
Such a graph depends on sound level: it becomes flatter at high sound levels. 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? Intensity, radiation and dB How does sound level or radio signal level, etc depend on distance from the source? So, if we double the distance, we reduce the sound pressure by a factor of 2 and the intensity by a factor of 4: in other words, we reduce the sound level by 6 dB.
If we increase r by a factor of 10, we decrease the level by 20 dB, etc. 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: why emit a substantial fraction of power upwards if the receiver is, like you, relatively close to ground level.
For sound of short wavelength including most of the important range for speech , a megaphone can help make your voice more anisotropic. For radio, a wide range of designs allows antennae to be highly anisotropic for both transmission and reception.
Example problems A few people have written asking for examples in using dB in calculations. All else equal, how much louder is loudspeaker driven in its linear range by a W amplifier than by a 10 W amplifier? I am standing at a distance R from a small source of sound size much less than R , at ground level out in the open where reflections may be neglected. The sound level is L. If I now move to a distance nR n a number, and nR still much greater than the size of the source , what will be the new sound level?
If, in ideal quiet conditions, a young person can hear a 1 kHz tone at 0 dB emitted by a loudspeaker perhaps a softspeaker?
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