SPL formula

Discussion in 'Archived Threads 2001-2004' started by Bob_M, Feb 8, 2001.

  1. Bob_M

    Bob_M Stunt Coordinator

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    Hi all,
    What is the formula for calculating total watts needed to reach a given SPL with a given Speaker sensitivity? I can write a table but just can;t get the forula worked out. thanks Bob
     
  2. Bob_M

    Bob_M Stunt Coordinator

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    I think I got it:
    SPL = Sensitivity + 10 (log(watts))
     
  3. Eric S

    Eric S Agent

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    Alternatively, if you don't have a calculator handy, start with the speaker's rated sensitvity at 1 watt, and just add 3 dB each time you double the power.
    For speakers with 90dB efficiency, just double the power each time until you ballpark your amp:
    1 watt = 90 dB
    2 watts = 93 dB
    4 watts = 96 dB
    8 watts = 99 dB ... and so on. Not as exact as the formula, but it will get you close enough.
     
  4. Greg Monfort

    Greg Monfort Supporting Actor

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    Yes, this is correct for just this value, but for comparisons at different powers:
    SPL = sens + [10*(log P2/P1)]
    where:
    P2 = peak power
    P1 = reference power (1W in your case)
    If you want to know how much power is required for a given SPL, then:
    P = 2^[(dB2 - dB1) / 3.01]
    where:
    dB2 = peak SPL
    dB1 = reference SPL (speaker sens in your case)
    GM
    ------------------
    Loud is beautiful, if it's clean
     
  5. Robert Fellows

    Robert Fellows Stunt Coordinator

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    Bob:
    Email me and I'll send you an Excel graph/table.
    ------------------
    Bob
    p.s.: This advice is worth exactly what you paid for it...
     
  6. Bob_M

    Bob_M Stunt Coordinator

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    Hi Greg,
    >P = 2^[(dB2 - dB1) / 3.01]<
    How did you come up with this? Can you get that by solving for P in the SPL equation, SPL = Sens + 10 (log(p))?
    Thanks Bob
     
  7. Greg Monfort

    Greg Monfort Supporting Actor

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    I got it from a long out-of-print book. [​IMG]
    Yes, it's derived from: dB = 10*[log(P2/P1)],
    which is a different way of expressing:
    y = 10*{log[x^(10*log2)]/log2,
    and P = 2^[(dB2 - dB1)/3.01] is from:
    x = 2^[y/(10 log 2)]
    where:
    x = change in power (new power/old power)
    y = change in dB (new dB - old dB)
    BTW, the 'P' in SPL is for 'pressure', not power. For 'sound power level', the abbreviation is PWL.
    GM
    ------------------
    Loud is beautiful, if it's clean
     
  8. Rob Roth

    Rob Roth Stunt Coordinator

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    Using this formula indicates that my 150wpc receiver will achieve clean levels of 108 dB with 87 dB sensitivity speakers. Actually, I doubt the power supply would handle the combined load. Are these instantaneous levels or sustained? Is the reference standard of 105 dB for peak or sustained?
    thanks
     
  9. Greg Monfort

    Greg Monfort Supporting Actor

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    This is transient peak power, unless you're playing sine waves. [​IMG]
    Since the peak-to-average SPL varies with frequency, the average 'loudness' without the amp clipping will be based on the 250-500Hz BW (assuming no organ music), which has up to 30dB peaks in music, reducing max average SPL to ~79dB, or 20dB for movies/~89dB/m.
    HT reference is 105dB peaks for all speakers, except the sub, 'at the listening position'. So if you're not within
     

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