How do sound decibels add together?

Discussion in 'Pro Audio' started by Tim Sprout, Aug 29, 2014.

  1. Tim Sprout

    Tim Sprout Guest

    If you play two sounds simultaneously, each at 100 decibels, what would
    a decibel meter read? 100 decibels?

    Tim Sprout
    Tim Sprout, Aug 29, 2014
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  2. "Tim Sprout" wrote in message
    Assuming the sounds are uncorrelated, the powers add: 100dB + 100dB = 103dB.
    William Sommerwerck, Aug 29, 2014
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  3. Tim Sprout

    PStamler Guest

    What William said. That's roughly how sound levels (dB-SPL) add. If the two levels aren't identical it gets a little more complex.

    PStamler, Aug 30, 2014
  4. "geoff" wrote in message
    ??? Why should they be?

    The powers of two uncorrelated signals simply add -- that's a fact. 100dB +
    100dB = 103dB

    Correlated signals -- I don't remember. I'd have to dig out a book.
    William Sommerwerck, Sep 1, 2014
  5. Tim Sprout

    Sean Conolly Guest

    My precarious and aging memory agrees with Geoff. If the signals are
    correlated with zero phase difference you add 3db. If they are out of phase
    then less, or even attenuation.

    But if we sum equal levels of random noise, I'd guess at any given moment
    you'd have slightly less than 3db, but when averaged over time the signals
    are would still would add 3db when summed.

    Then again, I've been having my share of 'senior moments' today.

    Sean Conolly, Sep 1, 2014
  6. Correlated and in-phase, they will add to give an increase of 6dB

    Correlated and out of phase, they will cancel, the degree of
    cancellation depending on the accuracy of the phasing and amplitude.
    Adrian Tuddenham, Sep 1, 2014
  7. Tim Sprout

    Don Pearce Guest

    Correlated signals will add to 106dB if in perfect phase - right down
    to - infinity dB if perfect antiphase

    Don Pearce, Sep 1, 2014
  8. Tim Sprout

    Scott Dorsey Guest

    This is correct for powers, which is what we are talking about when we
    talk about SPL.
    I believe it is 1.5dB for adding uncorrelated noises with the same spectra
    and the same average amplitude.

    All of this is fairly clumsy, because Bels, being a logarithmic scale, are
    not really intended for summing. They exist to make multiplying easier.
    Often if you have to sum values it's easier just to work back from SPL to
    pressure level in pascals and sum pressures (or back to volts or watts or
    what have you).
    Scott Dorsey, Sep 1, 2014
  9. "Sean Conolly" wrote in message
    If they were always "slightly less than 3dB", then they could never be 3dB
    over the long term.
    William Sommerwerck, Sep 1, 2014
  10. Just to avoid confusing the uninitiated:

    Double the voltage = quadruple the power = +6dB

    Always relate dB back to power and then it will make sense with less
    chance of an error. I know it's pedantic, but it avoids a lot of the
    misunderstandings which can occur if the 'power' step is left out of the
    Adrian Tuddenham, Sep 2, 2014
  11. Tim Sprout

    Les Cargill Guest

    Avoiding burning something up is hardly pedantry.
    Les Cargill, Sep 2, 2014
  12. Tim Sprout

    Tim Sprout Guest

    So...loudness is power based, logarithmic. A stadium of 50,000 cheering
    people generates power, which increases the loudness, with some
    attenuation depending on phase, and is not 50,000 X the loudness of 1
    person cheering.

    Thanks. I have always wondered about this.

    Tim Sprout
    Tim Sprout, Sep 2, 2014
  13. Just to chuck a spanner in the works, it depends what you mean by

    The power of a sound is the oscillating pressure change multiplied by
    the oscillating particle velocity. The capsule of a SPL meter measures
    the pressure change and then assumes the velocity change is proportional
    to that. Therefore, if the sound power is calculated by multiplying the
    pressure change by the velocity change, the power is proportional to the
    square of the pressure change (or proportional to the square of the
    velocity change if you measured it with a ribbon mic). This is why the
    scale on a common-or-garden analogue SPL meter is not marked linearly:
    it has to take account of the square-law relationship.

    If you used a pressure capsule on a voltmmeter or oscilloscope to
    measure the pressure, you would have to square the readings to make them
    proportional to power.

    To come back to your cheering people, the power of their voices does add
    up linearly (assuming they are uncorrelated and all exactly the same
    distance from the mic), but the mic voltage from 50,000 people will be
    SQRT(50,000) times the voltage of one single person.

    Now to throw another spanner in the works. Suppose you had a single
    loudspeaker generating a given sound power and you added a second
    loudspeaker giving the same power but uncorrelated - you would expect
    double the sound power (+3dB) and you would be correct. Now drive the
    second speaker in exact correlation with the first and the theory says
    you would get +6dB, which is four times the power - "but that's
    nonsense!" I hear you say. However, each loudspeaker is now working in
    the pressure field generated by the other, so it is having to do twice
    as much work; which means that the theory stands up to reality.

    In practice, most loudspeakers are so inefficient that the actual sound
    power they deliver is just a tiny proportion of the total electrical
    power they absorb, so you you wouldn't notice much change in the loading
    on the amplifiers. You might find there isn't a 6dB increase in
    practice, because the increased loading on each loudspeaker may mean
    that it can no longer deliver as much sound power as when it was
    Adrian Tuddenham, Sep 2, 2014
  14. Tim Sprout

    Don Pearce Guest

    And bear in mind that most of those 50,000 are a long way from you.
    Only the nearest twenty or so people contribute in meaningful way to
    the loudness you hear. The rest just add the background sussuration.

    Don Pearce, Sep 2, 2014
  15. "Tim Sprout" wrote in message
    No. Loudness is a subjective measurement. It is not exactly related to SPL.
    William Sommerwerck, Sep 2, 2014
  16. Tim Sprout

    Don Pearce Guest

    A rough rule of thumb - all else being equal - is that you need about
    a 10dB increase in SPL for a subjective doubling of perceived
    loudness. This comes with a multitude of caveats.

    Don Pearce, Sep 2, 2014
  17. Tim Sprout

    Scott Dorsey Guest

    In an open stadium this is definitely the case; you can think of the top
    of the stadium as being infinitely absorptive. Sound just goes up and keeps
    on going. But in a closed reverberant basketball court it's not!
    Scott Dorsey, Sep 2, 2014
  18. Tim Sprout

    Don Pearce Guest

    We don't bother with basketball over here, but a large public swimming
    pool certainly proves this. Why do people insist on screaming when
    they swim?

    Don Pearce, Sep 2, 2014
  19. Tim Sprout

    Jeff Henig Guest

    Maybe you should stop throwing Babe Ruth bars into the pool, Don.

    (One of my fave movie pranks, BTW. Caddy Shack was a classic.)
    Jeff Henig, Sep 2, 2014
  20. Tim Sprout

    Don Pearce Guest

    Okay, not seen that movie, but | looked up Babe Ruth bars - couldn't
    find them. But I did find Baby Ruth bars, and even before I realised
    what the swimming pool prank must have been, I got what they looked

    What kind of a mind do I have?

    Don Pearce, Sep 2, 2014
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