Sound Pressure vs. Sound Power

[Texan]

I can see the mathematical difference between Sound Power and Sound Pressure, but what is the significance of sound power?

[DDF]

Hi,
Sound pressure is the sound level at one point in space. Sound power expresses the total efficiency of converting electrical input to acoustic output, over all points in space.

Take a hypothetical example where two speakers have identical on axis frequency response and sensitivity, but one is omni-directional, and the other is dipole. The omni would be more efficient since it radiates more total sound power.

The impact of sound power is more obvious in a reverberant room. A live room ensures that off axis radiation from all different directions will reach your ear. In the hypothetical example above, in a reverberant room, the omni will play louder since it has mor eoff axis radiation, and more power output.

Another example is a horn, say a shallow horn added on a dome tweeter. Adding the horn to the dome will increase the sensitivity of the tweeter in its lower frequency range. However, the sound power remains the same since the sensitivity increase comes from reducing the sound radiated off axis.

[billfitzmaurice]

However, the sound power remains the same since the sensitivity increase comes from reducing the sound radiated off axis.

-1. Horns do not work by merely reducing the radiation angle. They work by better matching the high radiation impedance of a driver to the low impedance load of the air, which increases radiation efficiency and therefore acoustic power output for a given electrical input.

A better way to explain SPL versus power is by space loading. An omni-directional source will show an axial SPL increase of 6dB with the change from free-space, ie., suspended in the air, to half-space, ie., placement on the ground. A wall within 1/4 wavelength reduces radiation to quarter-space, giving another 6dB axial SPL, while a second wall (corner loading) adds another 6dB. That's a total differential of axial SPL of 18dB between free-space and eighth-space, while power remains a constant.

As for a dipole versus monopole, power output is the same, SPL is not, due to phase cancellation.

[the kid]

I haven't understood a word of this...but I am glad you guys are here for little 'ol me when I need ya!

[DDF]

-1. Horns do not work by merely reducing the radiation angle. They work by better matching the high radiation impedance of a driver to the low impedance load of the air, which increases radiation efficiency and therefore acoustic power output for a given electrical input.

That's true for large horns, but in the example used for a shallow tweeter horn, the efficiency loading is pretty modest.

A better way to explain SPL versus power is by space loading. An omni-directional source will show an axial SPL increase of 6dB with the change from free-space, ie., suspended in the air, to half-space, ie., placement on the ground. A wall within 1/4 wavelength reduces radiation to quarter-space, giving another 6dB axial SPL, while a second wall (corner loading) adds another 6dB. That's a total differential of axial SPL of 18dB between free-space and eighth-space, while power remains a constant.

That is a better explanation!

As for a dipole versus monopole, power output is the same, SPL is not, due to phase cancellation.

The theoretical construct made was that omni and dipole also had the same on axis sensitivity, and were idealized. Given that there is phase cancellation with a dipole, useable power output couldn't be the same. Taking it to an extreme analogy to illustrate the point, placing two identical speakers face to face and out-of-phase results in nearly zero usable output, given there is almost no sound produced. Sound power is calculated as the energy flow through a closed surface surrounding the source. As integrated over a particular surface area in the room, it would be nearly zero in this extreme case. In a similar fashion, the phase cancellation with the dipole reduces the sound power compared to omni.

[Texan]

So?

If I have an omni source the sound pressure level will increase by 6 db if I move the source up to the wall, but the sound power will remain the same as the same amount of acoustic energy is radiated into the room?
This would seem the same if I had 2 sources. When the second source was added the sound power would increase by 3 db, but sound pressure would increase by 6db provided the sources are close to each other?

If sound power can be described as the rate of acoustic energy…? Then a speaker designed to take advantage of an increase in sound pressure that exceeds the increase in sound power, would not only be seen as an increase in efficiency by the listener, but would also allow for less room interaction due to the reduction of sound power at the same listening level.
As you can see this could develop into line array theory. What if we did not consider only expansion vertically, but…

What if an ideally beamy speaker was created such that the hypothetical listening area was the size of the listeners head, and the wall behind the listener was removed, then there would be no reflection from any wall ceiling or floor, and the listener would here only sound coming from the speaker, and nothing else. Also no one else in the listening room would be able to hear the speaker. Now we are headed for acoustic weapon theory.

Does every technique that yields a disproportionate increase in sound pressure over sound power result in reduced dispersion?
The two examples I can thank of are horns, and multiple subwoofers. Horns obviously reduce dispersion, but as bill pointed out that is not the only mechanism that increases their efficiency. Two subs would contribute as above, but assuming they were crossed over pretty low say 40hz then no reduction in dispersion would be noticed.

[DDF]

So?

If I have an omni source the sound pressure level will increase by 6 db if I move the source up to the wall, but the sound power will remain the same as the same amount of acoustic energy is radiated into the room?

Yup, assuming its onmidirectional to start with and if the distance from the wall is much shorter than the wavelength (Bill used the metric of < 1/4 wavelength). If its not Omni, or the distance was greater, it would be less than 6 dB. 6 dB is the maximum attainable.

This would seem the same if I had 2 sources. When the second source was added the sound power would increase by 3 db, but sound pressure would increase by 6db provided the sources are close to each other?

Pretty much. Its why less than 6 dB BDC is often targeted in stereo, since at lower frequencies, the two speakers add more coherently, increasing total SPL as frequency decreases.

If sound power can be described as the rate of acoustic energy…? Then a speaker designed to take advantage of an increase in sound pressure that exceeds the increase in sound power, would not only be seen as an increase in efficiency by the listener, but would also allow for less room interaction due to the reduction of sound power at the same listening level.
As you can see this could develop into line array theory. What if we did not consider only expansion vertically, but…

The design metric "Directivity Index" is used by the sound reinforcement world to describe the is reduction in off axis power , compared to a omnidirectional source. The optimum directivity index in a listening room has never really been determined, and would change with the recording or size and reverberation characteristic of the room.

BTW, directivity changes can be achieved by increasing effective on axis power at the cost of off axis (eg horns) or by dissipating some off axis energy as heat, with absorption (some cardioid implementations).

Does every technique that yields a disproportionate increase in sound pressure over sound power result in reduced dispersion?

A disproportionate increase in sound pressure over sound power means that the directivity index is increasing. This means that the sound is being directionally concentrated, but it doesn't say into what pattern. For example, cardioids and dipoles both have directivity indexes of 4.8 dB, but show very different dispersion characteristics in the frontal plane.

[Texan]

You guys seem to have it nailed. Thanks for the help. I will look up “directivity index”. Now all I have to do is find a way to use my now more in depth knowledge for evil.

[DDF]

You guys seem to have it nailed. Thanks for the help. I will look up “directivity index”. Now all I have to do is find a way to use my now more in depth knowledge for evil.

Someone already beat you to it.

http://www.spiegel.de/international/...385048,00.html