Sound power vs frequency response

[o2so]

Hi there, can any kind soul please explain to me in laymen's terms the physical difference between sound power and frequency response of a speaker? What does it mean when two different speakers have the same frequency response but different power at a given frequency, for example in the lower octaves? How does that translate into what we hear, assuming it does?
Thanks

 

[ADU]

Howdy, o2so. Have you seen this video by Floyd Toole, which discusses (among other things) the differences between a speaker's direct/on-axis response, its in-room response, and also its sound power response? If not, this might be a good place to begin to gain a little better understanding of some of the differences.

 

[NTK]

Sound power is the average of the radiated power from the loudspeaker in all directions. The most common method is to take measurements in a spherical surface all around the loudspeaker, integrate the measurements over the surface of the sphere, and then divide by surface area of the sphere to obtain the average power.

For ANSI/CTA 2034-A (aka spinorama), Frequency responses (FR) are measured at the 70 points in the vertical and horizontal orbits in 10 degrees angular spacing (i.e. 32 36 points for each orbit, with 2 shared common points = total of 70 FR measurements). For each frequency, each of the 70 measurements is weighted according to the portion of the spherical surface it covers, and the 70 weighted measurements are summed to give the sound power at that frequency.

The process is repeated for all frequencies. For FR measurements with 1/20 octave frequency resolution, the total number of frequencies is about 200 (10 octaves at 20 points per octave).

The weighting values are given in Appendix C of ANSI/CTA 2034-A. Note that we can't directly sum dB SPL values. They must be converted to sound pressure (unit: N/m^2) first, obtain the weighted sum, and then reconvert back to dB SPL for reporting.

You can download the CTA 2034 standard at no cost at this link (will need an email address for registration).

Standard Method of Measurement for In-Home Loudspeakers (ANSI/CTA-2034-A R-2020)

This Standard describes how to determine the frequency response, directivity and maximum output capability of a residential loudspeaker.

shop.cta.tech

Unless the loudspeaker is perfectly omnidirectional, the sound power will be different from the on-axis response. Since practically all loudspeakers are more directive at higher frequencies, their on-axis response will be higher than their sound power. The difference between the on-axis response and sound power is the sound power directivity index (SPDI). For example, when the SPDI is, say, 4 dB at 2 kHz, that means at 2 kHz the on-axis SPL is 4 dB higher than the sound power SPL.

[Edit] Correct errors.

 

[o2so]

Thank you. So it does not have anything to do with what I thought it had.
I hear the expression that a speaker with larger woofers "moves more air". I think this in audiophile jargon means that the bass notes have more "impact", at the same frequency and level of a speaker with smaller woofers.
Is this an actual measurable effect, or just fluff?

 

[NTK]

SPL is directly related to the volume of air being displaced. Volume displacement is equal to effective surface area (Thiele/Small parameter "Sd") times the travel of the diaphragm times the frequency (i.e. number of movement repetitions per unit time).

When people say "larger woofer moves more air", basically it is just saying for a larger woofer, its capability to displace air, and therefore SPL capability, is (usually) higher than that of a smaller woofer. IME this should be quite obvious. Since we often judge the "bass impact" by how we feel it with our chests, and a higher SPL will definitely do a better job at it, it is quite logical to equate high SPL capability to "more impact".

 

[NTK]

To elaborate a little bit further from post #3, here is an example of a theoretical calculation of the sound power directivity index of a dipole source.

The sound power DI is given using the formulas:

For a dipole and r = 1, the radiation pattern can be described using the real part of the spherical harmonic function, Re(Y_1^1(θ,φ)), where θ is the vertical/polar angle and φ is the horizontal/azimuthal angle. The on-axis response is given by θ = π/2 and φ = 0.

The numerator is the square of the pressure amplitude of the on-axis response at r = 1; the denominator is the square of the average of the pressure magnitude all around the surface of a sphere with r = 1. The 1/4π in the denominator is from the surface area of the sphere, which equals to 4π, and is used to convert the total sound power to the average sound power. The pressure magnitudes are squared to give power.

The computed result of the SPDI of a perfect dipole is: ~4.8 dB.

 

[o2so]

SPL is directly related to the volume of air being displaced. Volume displacement is equal to effective surface area (Thiele/Small parameter "Sd") times the travel of the diaphragm times the frequency (i.e. number of movement repetitions per unit time).

When people say "larger woofer moves more air", basically it is just saying for a larger woofer, its capability to displace air, and therefore SPL capability, is (usually) higher than that of a smaller woofer. IME this should be quite obvious. Since we often judge the "bass impact" by how we feel it with our chests, and a higher SPL will definitely do a better job at it, it is quite logical to equate high SPL capability to "more impact".

Thank you. So it is not possible to have greater impact at the same spl?

 

[NTK]

Thank you. So it is not possible to have greater impact at the same spl?

I don't think so.

 

[ADU]

I know when I'm out-matched on the technical stuff. And can't really say for certain what reviewers and other audiophiles mean when they refer to things like "impact".

But in addition to some of the things that NTK mentioned above, like the size, SPL, and stroke/excursion of the low frequency driver, some other things you might also look at in the measurements are things like the speaker's extension or rolloff in the lower frequencies, its resonant frequency, and also its distortion. A speaker with good extension, lower (or more optimal for the content?) resonant frequency, and lower distortion in the bass/sub-bass frequencies might, for example, be perceived as having greater impact than one without those characteristics.

The speaker's sound power and directivity can also give you an idea of how much energy it has in a room in the lower vs. the higher frequencies. A speaker with more low frequency energy (ie a higher sound power response in SPL) relative to the higher frequencies, might (emphasis on the might) also possibly contribute to its sense of impact. Even if its direct/on-axis response is still comparatively flat. (It's an interesting theory anyway. )

There could be other sound quality tradeoffs though to a speaker which has significantly more energy in a room in the lower frequencies though, like possibly a narrower listening window. I think it would sort of depend on how that LF energy was distributed though. If the sound power response and directivity is fairly smooth and linear, and the sound power only peaks significantly in the very lowest frequencies in the sub-bass and gradually falls off from their toward the higher frequencies, then the consequences in terms of other SQ tradeoffs may be minimal, and the results quite good. YMMV on this of course.

 

[DVDdoug]

I hear the expression that a speaker with larger woofers "moves more air"

Although a speaker does "move air" close to the speaker (and in & out of a port) that's not "sound".

Technically, a bigger speaker will compress more air than a smaller speaker with the same movement. A sound wave is moving compression and decompression of the air. So at the positive peak of the wave the air pressure is slightly-above normal atmospheric air pressure and the negative peak is slightly-below the normal level. It's kind-of difficult to visualize because we can't see it and don't really hear movement and we don't feel it as pressure in our ears... Our ears & brain convert the fast pressure-changes into "sound". It's the pressure-wave that's moving (at the speed of sound) not the air. Its the similar to waves in the water... The wave moves across the surface (and they can move a boat or a surfer) but if you do something like dye the water, you'd notice that the water is only moving up & down.

A smaller woofer "simply" has to make bigger movements than a larger woofer. The effective area of a speaker is called 'piston area" and just like a piston compressing air or pumping a liquid, a smaller piston needs more distance to get the same result.

A bigger woofer isn't always better. It depends on the design of the woofer & cabinet. But if you try to get a lot of deep bass from a small woofer you eventually run into the limitations of "physics". You're not going to get bass you can feel in your chest with a 5-inch woofer. And a kitten can't roar like a lion...

I think this in audiophile jargon means that the bass notes have more "impact", at the same frequency and level of a speaker with smaller woofers.

"Audiophiles" use a lot of nonsense jargon that seems to have a meaning but usually it's more about a feeling.

 

[ADU]

I'm already out of my depth on this subject. But perhaps front vs. rear porting might also make some difference. (?)

 

[Tom C]

The way it’s been explained to me, as others have said above, is that what’s important is the volume of air displaced by the speaker. So a larger diameter driver has to travel less along its axis to displace the same volume of air as compared to a smaller diameter speaker. Since there are practical limits as to how long a path a voice coil can be made to travel along its axis, it is more common for a larger diameter speaker to give high output in the bass (slam) vs. small diameter woofer.
The biggest difference between rear port and front port is what happens as you place the speaker closer to the wall. There will always be more reinforcement of bass output from the wall, but the effect should be greater with a rear ported speaker. Output from front ported should increase less as you place it closer to the wall.
I had a pair of rear ported speakers, though, that had low bass output no matter what you did. Increasing the EQ in the low end just made the distortion go crazy. So, without a doubt, some designs are better than others.

 

[NTK]

Thank you. So it is not possible to have greater impact at the same spl?

Thought about it a little bit more, and I remember that frequency response error can also manifest as "slow, flabby bass".

Here is an example of the responses to a resonance with a peak gain of 6 dB and a Q of 5, at the normalized center frequency of 1. Below is the frequency response (magnitude) that shows the resonance.

Below is its time domain response to a 16 cycles sine burst at the resonance frequency. The amplitude of the output went higher than the input due to the resonance. You can see that, for this particular case, it takes about 8 cycles before the resonance reaches its steady state output amplitude. When the input signal ends abruptly, the response again takes many cycles to decay. This type of response from resonances, which takes time to build up and time to dissipate, often appears to us in the bass frequencies as sounding slow and flabby (as oppose to crisp and tight).