Sound Pressure Level and NASA

Many audiophiles love to "turn it up" and hear their rigs at the maximum sound pressure level (SPL) that it can achieve within tolerable distortion limits. Car audio has even added contests for the loudest stereo and given awards for the most ear-shattering systems. But what is the theoretical loudest sound that can be achieved?

One may think that this is a never ending possibility; all you need is more drivers, and more power. Not so! The medium we use to hear is air and there is a limit as to how much something can make this elastic gas move back and forth. As it is with flexible things, there is a point to where you can mash and stretch them and then they break. With gasses such as air, the same is true and even if you add more power, the sound doesn't get any louder.

Fortunately, this point is well beyond the threshold of pain and should never be attempted to achieve (such as at ground zero of a nuclear explosion), but just for grins what is the number associated with that sound?

The calculation goes like this for an average air pressure of 101325 Pa :

L = 20 × log (101325 / 0.00002) = 194 dB (RMS)

WOW! now that's loud! Even at the loudest rock concerts, sound pressure levels of this magnitude are only achievable in the minds of fanatics.

A long time back (in the early 1970s) NASA did an interesting experiment in trying to understand the impact of loud noises on things. Rocket launches produce sound pressure levels close to this physical limit and it was their concern that these vibrations could do some real harm, other than deafen an astronaut. They were right. But how did they do this without investing in a jigawatt flux capacitor? Someone came up with a brilliant idea.

Most audiophiles know that horns literally transform whispers into roars. If you go to any concert that uses sound reinforcement, you will see horn stacks suspended along the stage. Horns are acoustic transformers that allow the severe mismatch in power transfer of a speaker driver to better couple it to the characteristic impedance of air. Just like matching transformers on tube amplifiers that match the electrical output impedance of the tube to the speaker impedance, horns do the same for matching acoustic impedances.

 

A Typical Horn Loudspeaker

Normal acoustic horns use one driver at the small end called the "throat"  (the hole at the back of the image above) and sound comes out the front end (called the "mouth"). Horns use an exponential relationship where the area doubles every unit. So at the throat, an area could be two square inches (two to the first power). Moving forward one inch, that area becomes four square inches (two to the second power, or two squared). Moving forward again one inch, that area becomes eight square inches (two to the third power, or two cubed). That's enough of the math for now, let's get back to how NASA did this test.

The great thing about any transformer, electrical or acoustic, is that it is bi-directional, that is, you can use either end as the input and the other end as the output. So NASA used this understanding and instead of driving the acoustic horn transformer using one driver from the throat (small end), they used tens (or was it hundreds?) of drivers at the mouth (large end) and put microphones at the throat.

Great idea. Now you can transform whatever maximum SPL of each driver is and combine that to produce a really loud sound pressure. It worked. What came about from these experiments is the water spray that comes on just before the engines fire and changes the density of air. The water does not keep things from melting down (although this is a side benefit), it actually lowers the maximum SPL created by the rocket engines.

So what should the sights of an audiophile's system be? How loud should it go to achieve realism? Should it be "toned down" so as to not produce pain or introduce instant hearing loss?

All excellent questions since people who own car systems capable of producing extreme SPLs can attest (current world record SPL in a car stereo is 174.1dB). A reasonable assumption would be loud enough to thrill you but not so loud as to harm you. But the maximum recommended SPL varries with time (how long you listen or are exposed to the sound) and how close you are to that sound. Here is a chart of what sounds commonly occur in nature:

dBA	Event
190	Heavy weapons, 10 m behind the weapon (maximum level)
180	Toy pistol fired close to ear (maximum level)
170	Slap on the ear, fire cracker explodes on shoulder, small arms at a distance of 50 cm (maximum level)
160	Hammer stroke on brass tubing or steel plate at 1 m distance, airbag deployment very close at a distance of 30 cm (maximum level)
150	Hammer stroke in a smithy at 5 m distance (maximum level)
130	Loud hand clapping at 1 m distance (maximum level)
120	Whistle at 1 m distance, test run of a jet at 15 m distance
	Threshold of pain, above this fast-acting hearing damage in short action is possible
115	Take-off sound of planes at 10 m distance
110	Siren at 10 m distance, frequent sound level in discotheques and close to loudspeakers at rock concerts, violin close to the ear of an orchestra musicians (maximum level)
105	Chain saw at 1 m distance, banging car door at 1 m distance (maximum level), racing car at 40 m distance, possible level with music head phones
100	Frequent level with music via head phones, jack hammer at 10 m distance
95	Loud crying, hand circular saw at 1 m distance
90	Angle grinder outside at 1 m distance
	Over a duration of 40 hours a week hearing damage is possible
85	2-stroke chain-saw at 10 m distance, loud WC flush at 1 m distance
80	Very loud traffic noise of passing lorries at 7.5 m distance, high traffic on an expressway at 25 m distance
75	Passing car at 7.5 m distance, un-silenced wood shredder at 10 m distance
70	Level close to a main road by day, quiet hair dryer at 1 m distance to ear
65	Bad risk of heart circulation disease at constant impact is possible
60	Noisy lawn mower at 10 m distance
55	Low volume of radio or TV at 1 m distance, noisy vacuum cleaner at  10 m distance
50	Refrigerator at 1 m distance, bird twitter outside at 15 m distance
45	Noise of normal living; talking, or radio in the background
40	Distraction when learning or concentration is possible
35	Very quiet room fan at low speed at 1 m distance
25	Sound of breathing at 1 m distance
0	Auditory threshold

Understand that the longer you listen to music, the quieter it should be. If you work in a noisy environment, use ear protection and do not drown out the ambient noise with loud music from your iPod.

My point is this: It may be nice to drown out the surrounding noise by turning up your music, but know that in doing so you can easily damage your ears. IMHO as an audiophile, absolutely nothing is worth that!

Yours for higher fidelity,

Philip Rastocny

I do not use ads in this blog to help support my efforts. If you like what you are reading, please remember to reciprocate, My newest title is called Where, oh Where did the Star of Bethlehem Go? It’s an astronomer’s look at what this celestial object may have been, who the "Wise Men" were, and where they came from. Written in an investigative journalism style, it targets one star that has never been considered before and builds a solid case for its candidacy.

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