Wednesday, August 29, 2007

How Much Power Do I Need?

Have you ever wondered how much power you will need from your amplifier to drive your loudspeakers?

Maybe this information will help you figure this out.

Amplifier power is usually given in watts, which is the amount of energy expended in one second (1 joule per second). In electrical terms 1 watt is equal to 1 volt multiplied times 1 ampere. Not sure if that helps here, because this doesn't seem to directly relate to how much sound you can generate with an amplifier. We usually measure the loudness of something using decibels or dB. The dB uses the logarithmic (base 10) scale because that is how our ear/brain perceives sound changes. Theoretically, the smallest change in sound level the human ear can perceive is 1 dB.

The following chart shows the amount of dB per watts ((dBW), which will make it a little easier to relate the amplifier's power rating to the amount of sound it can provide:

As you can see from this chart, an increase of 3 dB results in a doubling of power. So to handle an increase in dB from 23 to 26dB, you will need to double the power from 200 to 400 watts. To be able to notice the next incremental increase in loudness, you would need to go up to 500 watts.

Another factor that we need to consider is -- How loud do you need to go? That depends on your listening preferences. If you normally listen at fairly quiet levels, you don't need a lot of power, but if you like listening to rock music at live concert levels, then you may need a lot. Here's another chart (I love charts) to show how the dB relates to different sound levels:

Decibel (dB) level
Cause or Effect
-80 (p)
Underwater nuclear submarine microphones listening to shrimp chewing on food at 100 meters distance
-30 (n)
One human talking 20 miles away (60 db / meter at a distance of 20 miles)
-4 to +4 (n)
The ticking of an ordinary wristwatch at 1 meter
0 (n)
Beginning of hearing, a mosquito 10 feet away, the ear drum moves less than 1/100 the length of an air molecule
10 (p)
Absolute silence, AT&T - Bell Labs "Quiet Room"
13 (p)
Ordinary light bulb hum
15 (n)
A pin drop from a height of 1 centimeter at a distance of 1 meter
30 (p)
Totally quiet nighttime in desert - impossible anywhere near city
35 (p)
Anechoic hearing test room
A whisper
A normal conversation
Average city traffic noise
Beginning of hearing damage (8 hrs), earplugs should be worn
Lawnmower, food blender
Normal average car or house stereo at maximum volume
104-107 (p)
The beginning of pain at the most sensitive frequency of 2750 hertz
Symphony orchestra
Human body begins to perceive vibration in the low frequencies
Home stereo system, a very loud and powerful 200-2000 watts
front row at a rock concert - up to 200 refrigerator size speakers and 50000-300000 watts of clean, full frequency sound
Drum set - only at the moment of striking, continous level 115
Human tinnitus (ringing in the ears) begins
128 (p)
Human, loudest scream measured at a distance of 8 feet 2 inches, head hair begins to detect vibration, can begin to detect very slow “blast wind” of 0.124 meters/second
130 (n)
Marching band - overall level at a distance, 100-200 members
Eardrum “flex” totally noticeable
133 (n)
Gunshot- ear level, may vary greatly to size and type of gun, duration converted to one second, peak level may reach 140-160
130-135 (n)
Large train horn
Human, a slight cooling effect begins to be noticed, from air expansion
Human body vibration is strong
Human ear all frequencies are painful
Extremely damaging to hearing no matter how short the time exposure, human throat and vocal cord vibration begins
Human body begins to feel nausea after a few minutes
Human body chest pounding is intense
Human body feels as if someone just football tackled your chest
Human nose itches
Human vision begins to vibrate making it slightly blurry, 1-3 degrees
Human vibration very uncomfortable and slightly painful
Human lungs and breathing begins vibrating to the sound
150 (n)
Rock concert “The Who” two 10 story stacks = 144 double refrigerator sized speakers, actual level reached 120 db at a distance of 32 meters for this normalized reading of 150 db. Continuous level 114-118db (p) at 32 meters
Human body vibration is violent, nausea becomes more intense
N.H.R.A. Dragsters- 5000 to 7000 horsepower, liquid nitroglycerin fuel, earthshaking at 50 feet, humans find it hard to see, and breathe 140db (p)
163 (p)
Glass breaking level, minimum, it is very hard to break glass windows. Many stories come from breaking glass but it is highly variable: it is easier to break if the window already has a crack, is very large or old and brittle and not car safety glass which can flex massively before breaking. An opera singer at 110 db may break a wineglass but it is an example of frequency resonance, and not high sound db level
145-165 (np)
Common type of fireworks at professional pyrotechnic shows
172 (n)
Boeing 727, 737, 747, 757, 767 cruising at 6 miles high mach 0.84, at the ground (sea level) loses an additional 6 db because air density is only half sea level at a height of 6 miles
Alan Dante reportedly set a new record in the world of in-car bass output by using four Stetsom 7KD amplifiers, 15 Power Master batteries, and a single Digital Designs 9918Z subwoofer.
183 (p)
6 p.s.i. Total destruction of all structures, particle velocity (blast wind) is 180 miles per hour. 0.9 miles from Hiroshima atomic bomb and 3.3 miles from 1 megaton nuclear bomb, less 0.1 % object survival
190.6 (np)
Richter scale 0 (zero) earthquake
190-195 (p)
Human eardrums rupture 50% of time
210 (np)
Richter scale 2.0 earthquake
215 (n)
Thunder, the largest positive giants. Ordinary thunder 165-180 db. Lightning strike on ocean surface 234db (p) at 2exp-5 newtons per square meter
240 (n)
Tornado, Fujitsu 5, energy guess based on 300 mile per hour wind, 1 mile wide
257 (n)
Nuclear bomb, 1 megaton (1 million tons of t.n.t.)
300 (n)
Hurricane – average, extreme energy is “diluted” by covering 500,000 square miles. Energy = approx. 1000 nuclear bombs a second.
320 (n)
Volcano eruption, Tambora Indonesia, 1815, ejected 36 cubic miles. Approximately equal to 14,000 megaton nuclear bombs or a 14 gigaton bomb based on ejected volume, change in megatons times 1.345 equals volume ejected change. If was a nuclear bomb it would create a crater about 12.4 miles wide and 1.33 miles deep. Internal pressure is believed to be about 47 million p.s.i. = 347 db (p)
(n) = Normalized total air power energy level sound plus any wind, watts or joules per second. These levels have been converted.
(p) = actual Peak pressure meter readings i.e. a force per unit area
(np) = Normalized Pressure used in explosive measurements, blast wind is not included
sources: Ultimate Sound Pressure Level Decibel Table, COPYWRITE WILLIAM HAMBY 2004, National Institute on Deafness and Other Communication Disorders.

Update 9/11/07: new entry for 180.5dB from Engadget post.

So, if you want to listen to your sound system at the same level as a symphony orchestra (I assume this is during a loud passage), you would want amplifiers with enough power to deliver around 110 dB. For rock concert levels, something between 120-130 dB. Most of the time you're probably not going to listen at these levels, especially for those of us who share their dwellings with other people, like wives, children, pets, plants, etc., etc. Maybe an amplifier that can provide 105 dB without clipping would be good enough, since you are probably listening between 85-90 dB most of the time. The dynamic range (the difference between the loudest and the quietest sound) for a good system should be from about 105dB down to maybe 35dB. This gives us a total dynamic range of about 70dB.

Now let's take this information and apply it to choosing the right size amplifier for your loudspeakers (if you like to do things ass backwards - you can also choose the right loudspeakers for your amplifier).
  1. You need to find the loudspeaker's efficiency or sensitivity specification. This is the sound pressure level (SPL) at 1 watt from a distance of 1 meter, given in dB. My Precise Monitor 10s have an efficiency spec of 88dB/1 watt/1 meter. My Era D5s use those 5" long excursion drivers that provide good bass for a small driver, but they are not super efficient with a spec of 86dB. There are a lot of speakers out there today with higher efficiency, but that doesn't mean they will sound better.

  2. Subtract about 10db SPL to account for the drop in sound level from the speaker to the listening position. (When you double the distance from the speaker, the SPL drops 6dB. The speaker's efficiency spec is based on a distance of 1 meter, and if the distance between the listening position and the loudspeaker is 2 meters, then the SPL drops 6dB. If this distance is 4 meters, the SPL will drop another 6dB for a total of 12dB. If the total distance is 10' (just over 3 meters) then the SPL will drop about 9dB.)

  3. Add 3dB for each additional speaker in the room that will be playing music at the same level (so when you do this calculation for a stereo system you simply add 3 dB).

  4. For my example with the Era D5s, I would get:
    86dB - 10dB + 3dB (for stereo music) = 79dB.

  5. Next, I need to calculate how much amplifier power is needed to get peak levels to 105dB without clipping.

    So I take the difference between the peak level and the loudspeaker value:
    105dB - 79dB = 26dB, which gives me the amount of power needed from the amplifier.

  6. Using the first chart, you can see that I will need 400W of power to get 26dBW.
Using this method, I would need about 250W to power my pair of Precise Monitor 10s. It gets a little more complicated when you try to calculate power requirements for multichannel 5.1 or 7.1 surround sound amplifiers. That's because the amount of sound from the surround speakers is usually less than the front right, center and front left channels. If you use bass management to send all signals below a certain frequency to a powered subwoofer, that will also decrease the power requirements of the multichannel amplifier. If I find a little more data on the most common multichannel surround mastering methods, maybe I will try to tackle this problem in a future post.

Here's a handy dandy dynamic slide rule that you can also use to perform these calculations.

Update 4/8/08: I discovered that Crown has a good article on their website to help you determine how much amplifier power is needed for your loudspeakers.

1 comment:

  1. 1. typical drop in SPL is not full 10db because the average listening room is not an anechoic chamber. actual drop may be more like 6db.

    2. musical peaks are much higher than most people think. well mastered recordings have peak-to-average of around 16-20db, so if listening at an average level of 95db, which is loud, you'd need a 115db capable speaker.