Paul's Posts — 20 February 2013


Music math

Thanks to reader John McRee for suggesting the title of today’s post.  Yesterday we learned we need 8 times more power to reproduce speech than we do sine waves – which may then surprise people that loudspeaker manufacturers continue to use sine waves as a basis for their efficiency measurements.  It certainly surprises me since we don’t listen to sine waves and one might question the value of such measurements.

If speech needs an 8:1 increase in amplifier power over sine waves, how about music?  Try 50:1 on for size.  The crest factor of music is generally around 20dB where speech is 12dB and sine waves are 3dB.  Remembering that each 3dB increase in crest factor requires the amplifier power to double, this means that a reasonably efficient loudspeaker, say 90dB efficient, needs 50 watts of power to reach musical peaks of 90dB, but only 1 watt to play the same loudness level sine wave.  50 to 1.

Now we should ask ourselves several questions: chief among them would be “what is loud”?  90dB is loud, that’s for sure, but if you’re listening to dynamic music, like orchestral, you can easily reach 100dB peaks when the orchestra plays loudly.

Our musical math would then show us if we need 50 watts to reach 90dB, we need 10 times that amount to reach 100dB!  That’s right, do the math.  For a 90dB pair of loudspeakers to produce 100dB peaks in your room without clipping the amplifier, you need 500 watts of power.

The average efficiency of loudspeakers is perhaps 87dB, and for such a loudspeaker you’d need 1000 watts to reach the same loudness without clipping.

So, what about more efficient loudspeakers?  Well, simply reduce the need back again.  If your speakers are 93dB efficient you need 250 watts, if they’re 96dB efficient you need 125 watts and so on.

One thing we haven’t yet covered is the distance from the speaker to the listener – because we must remember that all these figures in our musical math are based on sitting 1 meter away from your speaker (3 feet).  I don’t know about you, but I don’t personally sit that close to my speakers.  The further back you are the more power you need to reach the same level at your listening position.

Many of you are asking me if all this is true, which it is, how come my little 10 watt SET amplifier works just fine on my speakers?  Are tubes so much better at peaks than solid state that I am getting away with something?

Let’s take a look tomorrow at some surprising loudness figures and then start delving into amplifier types.

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About Author

Paul McGowan is the CEO and co-founder of PS Audio Inc. a Boulder Colorado design and manufacturing company of high-end audio products and services. McGowan has been designing and building high-end products for nearly 40 years. Hobbies include skiing, music, hiking, artisan bread baking, kick boxing and cooking. He lives in Boulder Colorado with his wife Terri and his 4 sons.

(5) Readers Comments

  1. This is very similar to the concept Antony Michaelson was promoting a few years back when he introduced his power boosters. The math made sense (and still does) but the industry never seemed to go along with it. The power booster was a flop and is now discontinued and low powered tube amps are still very popular. If the science ads up, why are the designers and market not following it?

    • That’s the $64,000 question, isn’t it? I’ll spend some time putting my opinion forward but to be honest I certainly don’t claim to have the answers other than what I think is going on.

      • I think I already mentioned a statement Bob Carver made about 25 years ago where he said in order to realistically reproduce the sound of just a simple pair of scissors snipping, he needed an amp with Thousands of watts of power! He was the original proponent of very high-powered amps… Sounds as if Bob was onto something!

  2. A couple of notes.

    We do not listen to human speech at 90dB, do we? That means we can use less power.

    I did a comparison. I took three short fragments (King Crimson, In the Court of the Crimson King, 24/96) and calculated the RMS and the crest factor:

    1. Loud – RMS -19.9 dB — resulting DR 11
    2. Quiet – RMS -29.6 dB — resulting DR 26.6
    3. Very loud – RMS -9.87 — resulting DR 9

    So, it all depends on what and where me measure. The higher the RMS (the louder the music) the less the crest factor, the less the headroom needed.

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