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Loudness vs. Power

Discussion in 'Amps and Cabs [BG]' started by mrjim123, Apr 2, 2013.

  1. mrjim123

    mrjim123 Supporting Member

    May 17, 2008
    Elkhart, IN
    The following presents an easily understood explanation of loudness vs. power: http://www.gcaudio.com/resources/howtos/voltageloudness.html

    Quick summary:

    * Doubling amp power increases loudness by a factor of 1.23 increase in loudness

    * To double loudness amp power must increased by a factor of 10

    Hope this helps a few folks.
  2. Hi.

    10 points and a star sticker for the effort, but all the hoping in the world won't help those "few folks" ;).

    And that's a definitive IME.

  3. KJung

    KJung Supporting Member

    This is correct and pretty well known. However, what gets confusing to many are the following points that are rarely discussed:

    1) What does 1.23 increase (approximately 3db) actually mean? Is it a lot or a little? (answer: it is actually quite a bit, but only happens when a speaker cabinet(s) can actually use the additional power, which is not always, or even often, the case)

    2) Doubling volume is kind of a meaningless target. That is approximately 10db (on the log db scale), and is massive.

    3) Increasing power is mostly about 'headroom', which is basically the concept of having the power to make the low notes and transient peaks (like digging in or slapping) sound the same (not compressed) through the night at the volume needed. This again assumes that the cab(s) can handle those transient peaks.

    So, the idea of simply thinking about doubling power providing a +3db increase is an oversimplification without taking into account the cabinet(s) capability, playing style (aggressive versus relaxed), tone goals (wide, deep and clean versus grindy, compressed and midrangey), and absolute wattage starting point (i.e., starting from a 'too low' amount of power to achieve the above versus' enough' power to achieve the above, relative to the cab(s) capabilities).

    To simply summarize... it all depends. Doubling power from 800 to 1600 watts into a 112 (as an extreme example) will result in zero increase in anything. Doubling power from 200 to 400 watts into a relatively low sensitivity 212 can be literally a life changing situation (a bit louder, much less compressed down low, better able to handle transients for an even, full tone).

    It all depends.
    Ewo, tonym, HolmeBass and 1 other person like this.
  4. No mention is yet made of losses from power compression.
    Also, the math mentioned above is primarily for small signal calculations, i.e. 1 watt or 2.83 volts below the onset of power compression.

    As power is increased, more power is consumed/wasted as heat. This waste does not make more noise.
    The onset of power compression comes at a surprisingly low power level.

    The JBL 2242H SVG is highly engineered to reduce power compression.
    The onset is a modest 80 watts, with a loss of 0.6 dB.
    At the rated 800w power, the loss is 3.3 dB.
    You can expect higher rates of power compression from lesser engineered drivers.
  5. KJung

    KJung Supporting Member

    +1 Much depends on the ability of the cab to handle additional power.

    On the other side of the equation, amplifier marketing power specs are all over the map regarding peak/burst capability, distortion levels at various power levels, power delivery across the full frequency range, and even more importantly preamp voicing/hi passing, which can have a massive impact on the way power is used, and also impacts the stress on the mechanical capability of the drivers.

    This is IMO why you get the almost bipolar discussions regarding this issue, with half stating 'you should have double the power of your cabinets thermal power rating to maximize performance' versus the other half saying 'you really can only use half the amount of watts suggested by the thermal power rating of the cab, since most drivers exceed their mechanical limits long before they reach thermal issues'.

    The reality, as with most things, kind of sits in-between those two extremes, and unfortunately depends on the correlation of amplifier power specs with reality, the hi passing and other baked in tonal profiles, and the actual power handling capability of the drivers.

    The impact of additional power depends on all this stuff, and unfortunately, most have to rely on TB reviews to sort it all out, since most of the combinations people are interested in are not available to try, except at the few brick and mortar 'bass only' stores that still exist.
  6. mrjim123

    mrjim123 Supporting Member

    May 17, 2008
    Elkhart, IN
    I hoped it would help a few of those few folks. The other few - well, you're right. :)

    And thanks to everybody else for the intelligent responses. At this point it would be nice to close the thread before those other few start spewing misinformation. :rolleyes:
  7. KJung

    KJung Supporting Member

    It is a very interesting topic, with lots of variables impacting the result. It can make you a bit crazy! Talkbass is just a wonderful place (with all the EE's that participate and all the real world reviews) for making sense out of the somewhat bewildering issue of why some rigs that look relatively the same on paper (based on the very limited specs presented by most manufacturers) perform so very differently.

    My rule is to ignore the posts by those who say more power never matters, and also ignore the posts by those who say more power is always worth the money/weight, etc. The truth is, as with most things, in-between those two extremes. This carries over to the 4ohm versus 8ohm cab discussion, which is also an 'it depends' situation that is highly correlated to this discussion:)
  8. One other point to keep in mind is that increases in dB at different frequencies don't equate to equal values of perceived loudness. Humans are most sensitive to frequencies between 200-5,000 Hz (those are the frequencies of human speech). Outside that range, either higher or lower, our sensitivity to increases in volume drops off. So, for example, below 100 Hz we may need quite a bit more of an increase in terms of dB to actually hear a difference, than we would at 1,000 Hz.
    HolmeBass likes this.
  9. +1

    I would also add that in addition to "It depends" there needs to be a lot of "Use common sense..." In cases where people are asking why they blew up their 108 cab using a 1,000 watt amp, or asking why they cant get loud/low enough with some cab that isnt designed to do what they want, there needs to be some understanding and realistic expectations.
  10. funnyfingers


    Nov 27, 2005
    Changing drivers isn't only about sensitivity though, but also the voice of the driver. My real world example is changing the Rumble 350 Combo with Eminence S2010s. I went from about a 5 in practice to 2.5. It is so clear. Partly it is just simply louder, but the clarity brings out the mids much louder as well. Also just played at a bar and I had it on 2.5 with the -6DB pad and no PA supporting me.
  11. Is there any psychoacoustics measuring to describe the relation between perceived loudness and frequency?

    Example A:
    -speaker A has 85 dB SPL/watt at 70 Hz on sensitivity magnitude
    -speaker B has 75 dB SPL/watt at 70 Hz
    What is 'exactly' the difference? Does it mean that the perceived loudness drops by half on B on this frequency?

    Example B:
    -speaker C has 85 dB SPL/watt at 500 Hz
    -speaker D has 75 dB SPL/watt at 500 Hz
    Perceived loudness drops by half on D at 500 Hz?
  12. el murdoque

    el murdoque

    Mar 10, 2013
    in short: yes. At 1W power from the amp and with your ear 1m in front of the cone.
    Provided, they used the exact same means of measuring.

    The problem with bass amplification is that the signal is so dynamic. You don't feed white noise into your amp, but a signal that has a wide range - both of power and frequencies used.
    And to top it off, the output of your amp strongly depends on the placement in the room and that is, in most cases, way less than ideal. Bass waves are long.

    Adding a second, identical cab to your setup will usually bring a total of 6db increase, 3db from doubling the speaker surface and 3db from the increase of power from the amp due to halved impedance.
    But in my experience, you get much more. There's more air being shifted around, resulting in a much fatter low end, even at lower volumes.
    I learned that when i added another GS212 cab to my tonehammer500 + GS212 and suddenly had to dial back on the bass knob.
    Reading up on the forums is helping, but personal experience is priceless.

    As said lots of times before - you can combine any type of speaker with any type of amp if you use your common sense (meaning that you don't dime your 1200w head when there's a 200w 112 cab attached) and stay within the given limits. If that is not enough, spot the weak link and invest there. You have a solid, poweful cab that is big enough for the job, but a weak amp and you don't cut through, a more powerful amp will be the cure. With crappy speakers, more power might just bring more farting.
  13. Ric5

    Ric5 Supporting Member Commercial User

    Jan 29, 2008
    I convert 4 string Rickenbackers to 5 string basses.
    Sometimes adding a 2nd cabinet will double your output.

    If you are running 1 8 ohm 2x10 cab and you add a 2nd 8 ohm 2x10 cab then the amp output will approximately double (actually a little less) and the speaker output will increase as well.
    Zooberwerx likes this.
  14. To clarify. That doubles the power your amp can output, but it does not double the sonic output. Adding a second matching cab gives you 3 db for the increase in power, and an additional 3 db for the increase in sensitivity for a total of 6 db increase. 10 db is considering doubling your volume.
    Zooberwerx likes this.
  15. Zooberwerx

    Zooberwerx Gold Supporting Member

    Dec 21, 2002
    Virginia Beach, VA
    This is one of the better "real world" applications / approaches and great stock response when asked "...will my 2 X 10 keep up with XYZ band?".

    Oh, yes...stack vertically but that's already being discussed in another thread.

  16. Actually, all my amps play too much bass freqs, I almost alwas turn the lows down. My limited experience says that bigger box makes the spectrum feel wider with clearer details on bass and - which i always wonder how important it is - on highs. I played some big Mesa Boogie bass box in a small club recently and it just had so many lows, that the mids and hight were unimportant. They were there, but the sound was without feel - deadly, but not really beautiful. I may be wrong, but I'm thinking that a super small cab can 'transfer' more feeling into the overall sound than a big bass beast.

    My question however aims to describe the differences between speakers. If I change the speaker, would I be able to hear the frequency difference? How much does the sensitivity magnitude really correspond to what I hear? What difference in dB SPL/w is audible? I have a feeling that the dynamics of loudness perception highly depends on frequency. +6dB on 3kHz is a big difference loud; +6dB on 70 Hz feels like nothing. Surprisingly, I haven't found on the net much on this topic. Articles on percepted loudness almost always ignore relationship to frequency. Why?
    I know I discuss here only one factor of many, but why not?
  17. beans-on-toast

    beans-on-toast Supporting Member

    Aug 7, 2008
    To give you some perspective, let's look at the math for a 100W, 200W and 300W amp and see how the dB numbers compare.

    Power = Voltage * Current
    Voltage = Current * Resistance
    combine them and Power = Voltage * Voltage / Resistance or P = V * V / R

    With a sine wave generator plugged into the input of the amp, you can drive it to full power and do the following calculations:

    For a 100W amp into a 4 ohm cabinet, P = V * V / R so V * V = 100W * 4Ω or V(RMS) = 20. The current will be 5A.
    So with a sine wave fed into the a 100W amp connected to a 4 ohm cabinet at full power, the voltage on the output is 20V.

    For a 200W amp, the voltage will be 28.3V, plugging into the formula above, the current is 7.1A.
    For a 300W amp, the voltage will be 34.6V, the current will be 8.65A.
    It's interesting what an extra 14.6V and 3.65A can do in going from 100W to 300W.

    Now another formula, to convert a change in voltage to decibels, dB=20 * log(V2 / V1). The same formula can be used for power, substitute P for V.
    In the case of a 100W to a 200W amp, the change in power is 2 times and the change in voltage is 20 * log(28.3/20) = 3.01dB.
    In the case of a 100W amp compared to a 300W amp, the change in power is 3 times, the change in voltage is 4.76 dB.

    Those numbers don't mean a lot to most players. You can hear a big difference between a 100W and a 300W amp. Sound pressure and volume perception is something else and more complicated.
    Last edited: Jul 8, 2014
  18. chaosMK


    May 26, 2005
    Albuquerque, NM
    Hi-fi into an old tube amp
    I find the massiveness of the cabs involved and EQ approach has the biggest impact on loudness once you get into a certain range (maybe 4-600w+).
  19. el murdoque

    el murdoque

    Mar 10, 2013
    How comes that the difference between 100W and 300W add up to 53,4W ?
  20. wlater


    Mar 13, 2014
    North Alabama
    Your formulas are right but I'm afraid you did your math wrong. 100W into 4Ω is 20 volts and 5A. P=I^2R=(5*5)*4=25*4=100W. Your numbers (20*20)*4=400*4=1600W

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