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Threshold of hearing: the smallest perceptible sound. A Sound Pressure Level (SPL) of 0.0002 dynes/cm 2 is the Common suffixes in the audio industry are: Where this is the case, a suffix is usually used to indicate the value that is being used as a reference (e.g. Sometimes the decibel is used to compare measured values to a single fixed reference value (or to state values with respect to that value). You can find functions to carry out most of the above calculations without needing the formulae or a calculator on our System Calculations page. Yet using decibels we find that the increase is still the same: 6dB (10 × log 4 = 10 × 0.6 = 6). However, we have quadrupled the power generated.
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Using decibels we find that doubling the output voltage is an increase of 6dB (20 × log 2 = 20 × 0.3 = 6). If we double the output voltage (40 Volts) we find that the power generated is now (40^2)/4 Watts = 1,600/4 watts = 400 Watts. From this, we can calculate the power generated into a 4Ω load as (20^2)/4 Watts = 400/4 Watts = 100 Watts. Where power and pressure combine, the values remain consistent.įor example, an amplifier produces an output of 20 Volts. Multiply your reference value by 10^(n/20).įor example, if your microphone produces 2.6 millivolts, an increase of 60 decibels will produce 2.6 × 10^(60/20) millivolts = 2.6 × 10^3 millivolts = 2.6 × 1,000 millivolts = 2,600 millivolts = 2.6 volts.At 20 decibels below full output, your 100 watt system is only running at 1 watt! Negative values work in exactly the same way, so that if your system is rated at 100 watts, a reduction of 20 decibels (−20 dB) will produce 100 × 10^−(20/10) watts = 100 × 10^−2 watts = 100 × 0.01 watts = 1 watt. Multiply your reference value by 10^(n/10).įor example, if your system is rated at 100 watts, a 20 decibel increase represents 100 × 10^(20/10) watts = 100 × 10^2 watts = 100 × 100 watts = 10,000 watts!.to work out what value is n decibels larger or smaller than a reference value): This may be a measured value, or may be a common standard reference point (e.g. ‡ The first value is your reference value. Divide the second value by the first value.Find the logarithm (base 10) of the result.įor pressure (e.g.Divide the second value by the first value ‡.To calculate the difference in decibels between two values: *In case you wondered why you are multiplying by ten to find a tenth of a Bel, note that a millimetre is one tenth of a centimetre: you would multiply a measurement given in centimetres by ten to obtain the value in millimetres. Where P is the power in Watts, V is the voltage in Volts, and R is the resistance in Ohms)†. This reflects the fact that any power value corresponds to the square of a pressure value: Watts are calculated by squaring the voltage and dividing the result by the resistance: Volts, or sound pressure), and is calculated in the same way, save that the logarithm is instead multiplied by twenty. The decibel can also be used to compare pressure measurements (e.g. In all cases they are derived from the ratio between two measurements, and in all cases they are calculated by finding the logarithm of the ratio, and multiplying it by ten*. Powers (this function is usually denoted by a ‘ ^’ sign).ĭecibel values can be calculated from any power measurements that use a common linear scale (e.g.To work out the numbers for yourself, all you need is a calculator with: While this may sound complicated (the decibel is a fraction of the logarithm of a ratio), the relationship between the numbers is always the same (like the relationship between Celsius and Fahrenheit), and - like temperature - the real-world events that give rise to the numbers can usually be seen and felt, as well as measured and compared. The Bel (named after Alexander Graham Bell, who used a logarithmic scale to quantify power losses in long cables) is the logarithm of an electric or acoustic power ratio. What is a Decibel?Ī decibel is one tenth of a Bel. To understand the answer, we also need to know what a number expressed in decibels actually tells us. To make the question sensible, we need to ask in terms of comparison: ‘How many decibels is it greater (or less) than something else?’. The question ‘How many percent is the output of this amplifier?’ makes no sense: how many percent of what? On its own, the question ‘How many decibels is the output of this amplifier?’ makes no sense either. It is a mathematical tool for comparison (like percentage).
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Most confusion arises from the fact that - on its own - the decibel is not a unit of measurement at all. The unit most commonly used (and often misused, or at least misunderstood) to compare sound levels is the decibel (abbreviation dB). An Introduction to the Decibel and its Use in Live Sound Reinforcement