# Db and frequency relationship

### dB: What is a decibel?

Hertz is the standard unit of measurement used to calculate the frequency of The average, healthy human can detect sounds at the zero decibel level, but a. The decibel (symbol: dB) is a unit of measurement used to express the ratio of one value of a The extra factor of two is due to the logarithm of the quadratic relationship between 1 MSC corresponded to the loss of power over a 1 mile ( approximately km) length of standard telephone cable at a frequency of . dB and Amplitude. I. LOUNDNESS, INTENSITY AND AMPLITUDE. Just as there is a relation between frequency and the musically important quality called.

According to Hickling, "Decibels are a useless affectation, which is impeding the development of noise control as an engineering discipline".

### Basics of Acoustics Hertz, cent and decibel

One advantage is that the total decibel gain of a series of components such as amplifiers and attenuators can be calculated simply by summing the decibel gains of the individual components. Similarly, in telecommunications, decibels denote signal gain or loss from a transmitter to a receiver through some medium free spacewaveguidecoaxial cablefiber opticsetc.

The decibel unit can also be combined with a suffix to create an absolute unit of electric power. 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.

## What is dB and frequency?

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. 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. It stands for one hundredth of an equal-tempered semitone. In other words, one octave consists of cents. An equal-tempered whole tone can be expressed as C, while an equal-tempered fifth would be C, or seven semitones.

Cents are used to express the size of individual microintervalsbut also to illustrate the ratio of any given interval such as a second or a third.

## Hertz, cent and decibel

The differences between the intervals of different tuning systems can be compared easily when the intervals are expressed as cents. 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 Hertz values can be converted to cents and vice versa by entering the values in the calculator below. Please use a point as the decimal separator.

Adjusting the frequency with a cent value: