# Relationship between decibel and frequency

### Decibels: dB Frequency Ohms Law When the frequency is in the range of several thousands Hz, the sound can still be The following equations hold true between frequency, wavelength and. dB and frequency are terms to describe sound level and the number of cycles Vibrations between 20 and 20, cycles per second are interpreted as sound. The decibel (symbol: dB) is a unit of measurement used to express the ratio of one value of a The decibel scales differ so that direct comparisons can be made between related power 1 MSC corresponded to the loss of power over a 1 mile (approximately km) length of standard telephone cable at a frequency of For example, it can be combined with "m" for "milliwatt" to produce the " dBm ". A power level of 0 dBm corresponds to one milliwatt, and 1 dBm is one decibel greater about 1. In professional audio specifications, a popular unit is the dBu. When used in a ohm circuit historically, the standard reference impedance in telephone circuitsdBu and dBm are identical.

Video and digital imaging[ edit ] In connection with video and digital image sensorsdecibels generally represent ratios of video voltages or digitized light intensities, using 20 log of the ratio, even when the represented optical power is directly proportional to the voltage, not to its square, as in a CCD imager where response voltage is linear in intensity.

Most commonly, quantities called "dynamic range" or "signal-to-noise" of the camera would be specified in 20 log dB, but in related contexts e.

Photographers typically use an alternative base-2 log unit, the stopto describe light intensity ratios or dynamic range.

### dB: What is a decibel?

Suffixes and reference values[ edit ] Suffixes are commonly attached to the basic dB unit in order to indicate the reference value by which the ratio is calculated. If the source is isotropic, the intensity I is the same everywhere on this surface, by definition.

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.

## Difference Between Decibel and Hertz

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: For sound of short wavelength including most of the important range for speecha 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. So, when you interested in emission in or reception from a particular direction, you want the ratio of intensity measured in that direction, at a given distance, to be higher than that measured at the same distance from an isotropic radiator or received by an isotropic receiver.

This ratio is called the gain; express the ratio in dB and you have the gain in dBi for that radiator. This unit is mainly used for antennae, either transmitting and receiving, but it is sometimes used for sound sources and directional microphones. Example problems A few people have written asking for examples in using dB in calculations. All else equal here means that the frequency responses are equal and that the same input signal is used, etc.

So the frequency dependence should be the same. To get a perceived doubling of loudness, you need an increase of 10 phons. I am standing at a distance R from a small source of sound size much less than Rat ground level out in the open where reflections may be neglected.

• Hertz, cent and decibel
• What is dB and frequency?

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 sourcewhat will be the new sound level? First, note that the neglect of reflections is very important. This calculation will not work inside a room, where reflections from the wall collectively producing reverberation make the calculation quite difficult.

The constant of proportionality depends on how well the ground reflects, and doesn't concern us here, because it will cancel in the calculation. An amplifier has an input of 10 mV and and output of 2 V.

What is its voltage gain in dB? Voltage, like pressure, appears squared in expressions for power or intensity. So, by convention, we define: 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.

What is the difference, in dB, between the irradiance light intensity on earth 8. Occupational health and safety 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 Afor 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 downbetween 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. Some FAQs How loud is an aircraft? The answers to this question vary considerably. It depends strongly upon how far away you are, whether you are indoors or not, whether there is reverberation, how strong the particular source is and what its spectrum is.

To give values, without being very specific about the conditions, would be somewhat misleading. Because the rest of this page is intended to be reliable, as far as it goes, I'd rather not give values here. How does one "add decibels"? If the sources are coherent which usually means that they ultimately come from the same sourcethen there may be complicated interference effects.

In most cases, where the sources are independent, one can add the intensities and then convert to decibels.

Frequency-Pitch and Amplitude-Loudness Relationship

However, if you are given the sound levels in dB Ait is not so easy to go back to intensity, and one must know something about the spectrum of the sound. In an equal-tempered system the intervals are always multiples of one hundred. The figure below shows a comparison of typical fraction notations of microintervals and the corresponding values in cents between the tones E and F. As the figure illustrates, a quarter tone is 50 C, while an eighth tone is 25 C. Fractions have traditionally also been used to express interval ratios. The use of fractions has been natural because the Pythagorean tuning system and the tuning system called just intonation are based on them. Comparing the fractions is, however, often more difficult than using the corresponding decimal values.

Fractions expressing interval ratios can be converted to cents using the following conversion formula: The logarithm of this value is approximately 0. When multiplied by k, the value is approximately In other words the pure fifth is two cents wider than an equally tempered fifth.

The pitch of the A3, for example, is Hz. A given interval will be very different in the lowest or the highest part of the hearing range. The range between 40 and 80 Hz and the range between and Hz both constitute an octave. The same interval can be expressed as a ratio in two different ways, but the higher figure is always the high tone.

The cent value can be converted to a decimal value by dividing it with the constant k and then inserting the result as the exponent of