What is Decibels: Definition and 41 Discussions

The decibel (symbol: dB) is a relative unit of measurement equal to one tenth of a bel (B). It expresses the ratio of two values of a power or root-power quantity on a logarithmic scale. Two signals whose levels differ by one decibel have a power ratio of 101/10 (approximately 1.26) or root-power ratio of 101⁄20 (approximately 1.12).The unit expresses a change in value (e.g., +1 dB or −1 dB) or an absolute value. In the latter case, the numeric value expresses the ratio of a value to a fixed reference value; when used in this way, the unit symbol is often suffixed with letter codes that indicate the reference value. For example, for the reference value of 1 volt, a common suffix is "V" (e.g., "20 dBV").Two principal types of scaling of the decibel are in common use. When expressing a power ratio, it is defined as ten times the logarithm in base 10. That is, a change in power by a factor of 10 corresponds to a 10 dB change in level. When expressing root-power quantities, a change in amplitude by a factor of 10 corresponds to a 20 dB change in level. The decibel scales differ by a factor of two, so that the related power and root-power levels change by the same value in linear systems, where power is proportional to the square of amplitude.
The definition of the decibel originated in the measurement of transmission loss and power in telephony of the early 20th century in the Bell System in the United States. The bel was named in honor of Alexander Graham Bell, but the bel is seldom used. Instead, the decibel is used for a wide variety of measurements in science and engineering, most prominently in acoustics, electronics, and control theory. In electronics, the gains of amplifiers, attenuation of signals, and signal-to-noise ratios are often expressed in decibels.

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  1. Juanda

    I 10^(1/10) is VERY close to 2^(1/3)

    Is there a subjacent reason that explains why these two numbers are so close? $$10^{1/10} \approx 2^{1/3}$$ For context, this is where I found out about this. Source: https://www.instarengineering.com/pdf/resources/Instar_Vibration_Testing_of_Small_Satellites_Part_5.pdf Is it just a...
  2. R

    Calculating Decibels & Watts: Looking for Help

    The above is just an example question to describe the situation. I am doing some simple calculations, but I think I am missing something. Is anyone here familiar with decibels? It is a coax cable and I'm working at ~20 kHz where attenutation isn't listed on the data sheet -...
  3. K

    Sound intensity - How to deal with decibels?

    I was looking up the maximal amount of noise allowed by current laws, that one can produce. I found that in my region one can produce sounds of up to 45 dB in the period from 22 pm to 7 am. But, it seems evident that the decibels fall off as we distance ourselves from the source. So shouldn't...
  4. B

    Decibel Intensity level question

    1. A jackhammer produces a sound of 111 dB IL. What is the sound level when 8 jackhammers are operating simultaneously? When 100 jackhammers are operating simultaneously? When 400 jackhammers are operating simultaneously?2. 1 jackhammer = 111 dBIL, 2 jackhammers = 114 dbIL, 4 jackhammers =...
  5. Const@ntine

    Sound Intensity (Level) - Hearing Aid

    Homework Statement A man is wearing a hearing aid device that increases the frequency of the sounds the human ear can conceive, by 30 db. The device "catches" a sound of frequency f = 50 Hz, and intensity I = 3.00 * 10-11 W/m2. What's the intensity that the man's ear hears? Homework...
  6. H

    Sound underwater distance and decibels

    I was wondering if sound underwater traveled further than sound in air? It seems like it wouldn't do to viscosity. I know that it travels faster however. Lastly, is the online reasoning for why we can't hear sound as well underwater correct: the water vibration bypasses some of the sensory...
  7. S

    Problem on Doppler effect and sound level

    Homework Statement A source emits a spherical sound wave at frequency ##f=110Hz## with power ##P=1 W## in a solid angle of ##2 \pi sr##. An observer moves with velocity ##v_{oss}=108 km/h## towards the source. Determine the sound intensity level received by the moving observer. Homework...
  8. D

    Calculating Power at source from Intensity at distance R

    Homework Statement An enclosed chamber with sound absorbing walls has a 2.0 m × 1.0 m opening for an outside window. A loudspeaker is located outdoors, 46 m away and facing the window. The intensity level of the sound entering the window space from the loudspeaker is 42 dB. Assume the acoustic...
  9. S

    Understanding a sound spectrum analyzer output

    Hi, I am just trying to understand the output of a sound spectrum analyzer. There are three dimensions 1) Time 2) Frequency 3) Volume (db) I am confused about few things here: 1) How should I perceive the volume dimension here? 2) Why are the db values negative here and w.r.t what reference...
  10. T

    Calculating Electric Field on Skin Surface with Decibels - Homework Help

    Homework Statement Let E1 be the electric field 1cm into a person's skin and E0 be the electric field on the surface of that person's skin. If the field loses -486db/m and E0 = 64.1, find the value of E1. Homework Equations E1/E0 = k, with k < 1 The Attempt at a Solution Well...
  11. K

    How far can your voice carry at 40 dB?

    You are in a park when you spot your friend 100 m away. At what lowest decibel should you shout your greetings so that your friend can just hear you? Assume that your friend has normal hearing. My prof never gave an example of how to do this and I can't figure it out. The correct answer is...
  12. S

    Why choose /100 over x100?Why Divide by 100 when solving decibels?

    I'm having difficulty understanding the solution to this question. "A source creates a sound that is observed at 200 Watts per meter squared. If the intensity level of the observed sound decreases by 20 decibels what is the decrease in observed intensity? The way I solved it was I saw 20...
  13. dexterdev

    Confusion in Power gain and voltage gain in decibels

    Hi all, I have a very basic doubt. If we have an amplifier with voltage gain A = Vo/Vi , where Vo is output and Vi is input voltages and Ap = Po/Pi which is power gain. Ap = Po/Pi = Vo^2/Vi^2 = (Vo/Vi)^2 In decibels powergain = 10 log (Po/Pi) = 20 log (Vo/Vi). In most tech...
  14. N

    Decibels, Waves, Kinetic Energy and Mosquitos

    Homework Statement A fan at a rock concert is 35.0 m from the stage, and at this point the sound intensity level is 115 dB . Sound is detected when a sound wave causes the tympanic membrane (the eardrum) to vibrate . Typically, the diameter of this membrane is about 8.40 mm in humans A) How...
  15. G

    Solving logs - Richter Scale and Decibels

    the text tells me that for calculating the Richter Scale magnitude of an earthquake we can use: M = log(I/I0) which can also be written as I = I0 x 10M Where M=magnitute, I=intensity, and I0=intensity 0 How are those two formulas equal? Where did the log go? Can someone show me the...
  16. D

    Reducing Decibel Levels: How Far Should You Move from a Loudspeaker?

    Homework Statement You are at a rock concert, standing 12.1 m from one of the loudspeakers. Based on the pain in your ears, you estimate the decibel level to be about 112 dB at this location. You are worried that this intensity level may be harmful to your ears and result in a degradation of...
  17. R

    Changes in Decibels over a distance

    Homework Statement A jet plane emits 3.0×105 J of sound energy per second. 1) What is the sound level 21 m away? 2) Air absorbs sound at a rate of about 7.0 ; calculate what the sound level will be 5.00. 3) Calculate what the sound level will be 7.50 away from this jet plane, taking...
  18. R

    Is there a formula to predict the loudness of an impact in deciBels?

    The question really explains the primary question but I have another quick one as well. How come sound isn't measured in Joules if it is a form of energy?
  19. J

    Sound intensity level, decibels

    A student typing in a computer cluster generates a sound level of 55 dB. What will the dB level the night before essays are due when there are 30 equally noisy students working in the cluster? dBo = 55 Ihearing = 1E-12 W/m2 Bo = 10log(I/Ihearing) 55 = 10log(I/Ihearing) 55 =...
  20. A

    Find Pressure amplitude from given decibels

    Homework Statement A sound wave has an intensity level of 49 dB. What is the pressure amplitude of this wave? Po= 2x10^-5 Homework Equations β=10log(I/I0) I≈P^2 The Attempt at a Solution I can't figure out why I'm getting this problem wrong. So I set it up, 49=10log(I/I0) ->...
  21. N

    How to Calculate Amplitude Using Decibels?

    I have got an assignment in which i need to compare wave interference, so i am going to use decibels readings which i had gotten from experiments and the reference amplitude which is 60 to calculate this very very confusing task. i have gotten these formulas derived from which i derived...
  22. C

    How do you convert from Decibels to SNR for use with Shannon's equation?

    Hi all, It's been many years since I did Mathematics last and I'm having trouble converting from db to the format required by Shannon's formula. I've googled and looked in the textbook but it's all a bit technical for me, I see logs and formula manipulation and go cross-eyed. I...
  23. T

    Adding dBm to dB from Rappaport's Wireless Comm.

    How does it become valid to add a dB with dBm? I found in a book that the author did like the following: 60dBm - 155 dB = - 95 dBm Isn't it necessary to convert 155 dB into dBm or vice versa and then doing the algebra? The book is wireless communication by Theodre Rappaport.
  24. M

    Converting Ratios to Decibels for Data Analysis

    I am analyzing sets of data in ratio form (0 to 1). My interest at the moment is the differences between 2 sets of data, let's say set A and set B. Initially I thought I wanted to analyze the data all in the form of ratios so all my means and SDs are calculated based on those ratios. Again, my...
  25. J

    Calculating Sound Wave Intensity and Decibels 10.0m from Source

    A source of sound emits 5.0 mW of acoustic power uniformly in all directions. 1. Calculate the intensity of this sound wave 10.0 m from the source. 2. Find the sound level in decibles 10.0 m from the source. Answers: 1. 4 x 10^-6 W/m^2 ---- I don't know how to get this answer. 2. 66 dB...
  26. 0

    How Close Must You Be to Double the Sound Intensity in Decibels?

    Homework Statement You are 10m away from a sound source. If you want the intensity in DB to double, you must move to a distance...? Homework Equations Idb = 10log(I/I0) I is proportional to 1/r^2 The Attempt at a Solution I know the answer is 1m and I know that in order to make...
  27. X

    How many decibels does a regular apartment wall cancel out?

    How many decibels does a regular apartment wall cancel out?
  28. X

    How many decibels is the sound of whispering laughter?

    How many decibels is the sound of whispering laughter?
  29. D

    How to calculate sound intensity when given decibels

    Homework Statement When a person wears a hearing aid, the sound intensity level increases by 30.0 dB. By what factor does the sound intensity increase? Homework Equations B = (10 dB) log (Ia/Ib) Ia = sound intensity Ib = threshold of human hearing (1.0 * 10^-12 W/m^2) The...
  30. A

    How Does Sound Intensity Change with Fewer Firecrackers?

    Homework Statement if two firecrackers produce a sound level of 95 dB when fired simultaneously at a certain place, what will the sound level be if only one is exploded? Homework Equations dB=10 LOG I + 120 The Attempt at a Solution would I use 2I instead of I making an equation...
  31. G

    Unit of sound/noise is decibels

    Hi all,i am extremely sorry that i am asking a very basic question,The unit of sound/noise is decibels,but unit of attenuation is also decibels/length, so how it could be possible as two are different things.
  32. Ed Aboud

    How do you convert watts per meter squared to decibels?

    Hi. How do you convert watts per metre squared to decibels? I know you use logs but can't seems to work it out. Thanks for any help.
  33. M

    Why is volume rated at 0 decibels?

    I got a Denon stereo receiver in this past year and I noticed that the volume meter starts at something like -70 decibels and moves up through 0 decibels. I've also noticed on other audio equipment that the 0 decibel rating is linked to some kind of amplifier power level or something. Why is the...
  34. A

    Decibels and intensity of police car siren

    I am struggling with understanding the difference between decibels and intensity. I know that intensity can be measure in decibels but they are not always the same thing. I have a problem where there is a police car 200 meters from an accident runing sirens at 80 decibels. I am asked to find...
  35. H

    Decibels, pressure & displacement amplitudes

    Homework Statement A jackhammer emits sound at a decibel level of 130 dB. The wavelength of the sound is 1.0 m. What is the linear sound intensity? What is the pressure amplitude? What is the displacement amplitude? Homework Equations Beta = 10 log (I / Io) ...and?? The Attempt...
  36. D

    How Do You Calculate Logarithms with Base 2 and Perform Decibel Calculations?

    logarithms and decibels please Hi i need some good tutorials for the logarithmsI(especialy for logarithms with base 2) and how i can calculate logarithms with base 2 when i have a simple calculator. Also i need some decibel tutorials that can help me understand how i can perform calculations...
  37. B

    What is the threshold for pain in decibels?

    1) what is a decibel? What is the threhold for pain in decibels? 2) what is a standing wave? 3) what produces sound waves? 4) Explain how the human ear receives sound and transmits it to the brain THANKS,
  38. G

    Medical How are decibels calculated on a logarithmic scale?

    I don't understand the math of the 10 fold system. Could someone go into detail of it for me? I just don't see how that works. 10 db = 100 20 = 1000 30 = 10000? i don't understand the system here.
  39. M

    Explaining Why 70 Decibels Don't Double in a Room

    Ok so will someone please explain to me why it is that when you have a machine that produces 70 decibels in a room and add an identical machine that also produces 70 decibels to that room, the decibels don't double... my book is very vague about this and does not explain it well... any help...
  40. S

    Why is 1 Decibel = 10 Log (Power1/Power2)?

    I know that 1 Bel = Log (Power1/Power2) and 1 decibel = 0.1 bel then why is 1 decibel = 10 Log (Power1/Power2) and not 0.1 Log (Power1/Power2) Thanks SK
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