gary f said:
If mounted in a box it is proportional to the acceleration.
The pressure from a point source is:
p=(U*rho0*w)/(4*pi*r)
where U is the volume flow (m3/s), rho0 is the density of air (=1.2 m3/s), w is the angular frequency (rad/s), r is the distance. Free field conditions are assumed. For low frequencies, a loudspeaker can be approcimated by a point source, and volume flow U is:
U=Sd*v
where Sd is the equivalent piston area of the speaker, and v is the velocity of the cone.
So p is oproportional to w*v which in turn is equal to the acceleration (with a 90 degree phase shift).
They do cancel, as a dipole speaker should. With a baffle width of 24", it will start cancellation around 280 Hz, and roll off at 6 dB/octave below that. Of course, with so much displacement to start with, you can still do 110+ dB @ 20 Hz...gary f said:
The concept was not only to make the wildest looking driver you've ever seen, but one with so much potential output that it's kind of a "so what" in terms of loss. There's so much to start with, you don't NEED a box.
Dan Wiggins
Adire Audio
OK, here we go.gary f said:
Sound pressure is proportional to the cone velocity.
Two examples, one real and one conceptual.
1.) A jet plane has broken the sound barrier and is now traveling at a constant speed of mach 1.X. The "sonic boom" is a sonic pressure wave created by the plane traveling at a contasnt velocity. The planes acceleration is zero.
2.) A speaker cone is driven by a triangle wave signal and the cone follows the signal perfectly. The cone moves at a constant velocity and changes direction instantaneously at the ends of its travel. Sound pressure will be generated by the movement of the cone and the SPL will be proportional to the cones velocity. If the SPL were proportional to the acceleration, the SPL would be infinite.
Re: Re: SPL function of speed or acceleration
Indeed...
What makes you think this? Are you saying that when fed with a square wave, the cone moves instataneously to the end position and stays there?
In its main frequency region a speaker cone is mass controlled, and the movement is controlled by a force, largely proportional to the driving voltage (a bit simplified, really the current). So F=ma tells us that the cone acceleration is proportional to the driving force, and since sound pressure is proportional to the driving voltage, it is also proportional to the acceleration, not the velocity.
It might be that this does not hold for the supersonic case, but I don't mind that.
roddyama said:
Indeed...
roddyama said:
What makes you think this? Are you saying that when fed with a square wave, the cone moves instataneously to the end position and stays there?
In its main frequency region a speaker cone is mass controlled, and the movement is controlled by a force, largely proportional to the driving voltage (a bit simplified, really the current). So F=ma tells us that the cone acceleration is proportional to the driving force, and since sound pressure is proportional to the driving voltage, it is also proportional to the acceleration, not the velocity.
It might be that this does not hold for the supersonic case, but I don't mind that.
Re: Re: Re: SPL function of speed or acceleration
The question isn't about the mechanics of the speaker but what is the parameter responsible for SPL. SPL is proportional to the peak velocity of the cone.
Certianly I understand it has to be accelerated to this velocity. I was trying to show that SPL is independant of acceleration. If you wish, you can reduce the acceleration in my scenerio above until you reach an acceptable level of acceleration. It will not matter how you change the acceleration as long as the cone reaches the same peak velocity, the SPL will be the same.
roddyama said:
"...one conceptual."Svante said:
The question isn't about the mechanics of the speaker but what is the parameter responsible for SPL. SPL is proportional to the peak velocity of the cone.
Certianly I understand it has to be accelerated to this velocity. I was trying to show that SPL is independant of acceleration. If you wish, you can reduce the acceleration in my scenerio above until you reach an acceptable level of acceleration. It will not matter how you change the acceleration as long as the cone reaches the same peak velocity, the SPL will be the same.
Re: Re: Re: Re: SPL function of speed or acceleration
Besides, as Svante pointed out, a triangular wave signal (voltage source) does not correspond to your triangular wave driver motion. You must go through the F=ma translation of force to motion.
No. Drivers are real, physical mechanicms, and have to follow the laws of physics. Show me a driver whose motion wrt time traces out a triangular wave, and I'll reconsider. Acceleration in your hypothetical example isn't infinite, because real drivers have real mass and real forces driving them. But, if a driver actually could reproduce a triangular wave, then it would have an infinite amount of high frequency content, and thus the SPL would be inifinite (proportional to acceleration).roddyama said:
"...one conceptual."
The question isn't about the mechanics of the speaker but what is the parameter responsible for SPL. SPL is proportional to the peak velocity of the cone.
Besides, as Svante pointed out, a triangular wave signal (voltage source) does not correspond to your triangular wave driver motion. You must go through the F=ma translation of force to motion.
sreten said:
A very fallacious assumption.
A bit like amplifier slew rate requirements - which is faster :
a) a 10W 10V/us amplifier or
b) a 100W 20V/us amplifier ?
some would say b) by definition, but IMO its a).
Uhhhhh ???????????
What has voltage rise per (micro)second to do with power?
About the SPL: Theory
According to JE Benson, who was Richard Small's (of Thiele/Small renown) PHD thesis advisor, in his book "Theory and Design of Loudspeaker Enclosures":
p(s) = eg(s)*rho*Sd*ad(s)/(4*pi*r)
p(s) is pressure
eg(s) is generator voltage
ad(s) is diaphragm acceleration
r is distance from the speaker
rho is air density
Sd is diaphragm area
SPL = 20*log10(p(s)/pref)
p(s) = eg(s)*rho*Sd*ad(s)/(4*pi*r)
p(s) is pressure
eg(s) is generator voltage
ad(s) is diaphragm acceleration
r is distance from the speaker
rho is air density
Sd is diaphragm area
SPL = 20*log10(p(s)/pref)
Sound pressure is the adiabatic particle displacment in an elastic medium (in this case air). This is the case regardless if the particle displacement is periodic or not and regardless of what is creating the particle displacement. It is the movement of the cone that causes the particle displacement regardless of what causes the cones motion.
The magnitue of the particle displacement is the instantaneous SPL at a point and is directly proportional the cone displacement over time, or cone velocity. This is true if the cone reaches that velocity in a short period of time (high acceleration), or if it reaches that velocity in a long period of time (low acceleration). Therefore the SPL is not directly dependent the cones acceleration.
The magnitue of the particle displacement is the instantaneous SPL at a point and is directly proportional the cone displacement over time, or cone velocity. This is true if the cone reaches that velocity in a short period of time (high acceleration), or if it reaches that velocity in a long period of time (low acceleration). Therefore the SPL is not directly dependent the cones acceleration.
Re: Re: Re: Re: SPL function of speed or acceleration
OK, reading your first post a second time I realise I missundestood what you meant. You start saying that the "A speaker cone is driven by a triangle wave signal and the cone follows the signal perfectly." This is not possible. The cone velocity does not follow the driving signal it follows the integral of it. In order to accelerate the cone from +<whatever> to -<whatever> you'd have to apply an impulse of infinite amplitude. I you could, this would induce an infinite impulse in the sound pressure as well.
So I still mean that SP is proportional to acceleration.
And if you think that "It will not matter how you change the acceleration as long as the cone reaches the same peak velocity, the SPL will be the same. " and you don't beleive my statement above, please try any loudspeaker simulation program that can plot cone excursion and compare it to the sound pressure. They will differ by 12 dB/octave, which would indicate a double integration, ie from acceleration via velocity to position.
roddyama said:
roddyama said:
"...one conceptual."
A speaker cone is driven by a triangle wave signal and the cone follows the signal perfectly. The question isn't about the mechanics of the speaker but what is the parameter responsible for SPL. SPL is proportional to the peak velocity of the cone.
Certianly I understand it has to be accelerated to this velocity. I was trying to show that SPL is independant of acceleration. If you wish, you can reduce the acceleration in my scenerio above until you reach an acceptable level of acceleration. It will not matter how you change the acceleration as long as the cone reaches the same peak velocity, the SPL will be the same.
OK, reading your first post a second time I realise I missundestood what you meant. You start saying that the "A speaker cone is driven by a triangle wave signal and the cone follows the signal perfectly." This is not possible. The cone velocity does not follow the driving signal it follows the integral of it. In order to accelerate the cone from +<whatever> to -<whatever> you'd have to apply an impulse of infinite amplitude. I you could, this would induce an infinite impulse in the sound pressure as well.
So I still mean that SP is proportional to acceleration.
And if you think that "It will not matter how you change the acceleration as long as the cone reaches the same peak velocity, the SPL will be the same. " and you don't beleive my statement above, please try any loudspeaker simulation program that can plot cone excursion and compare it to the sound pressure. They will differ by 12 dB/octave, which would indicate a double integration, ie from acceleration via velocity to position.
The SPL is related to many factors, but it is the cone velocity that directly causes the particle displacement and therefore SPL at a given point.SY said:
It is, I guess valid to speak of vibration, or periodic particle displacement since the original question specified a "transducer". WRT this, as the frequency and amplitude of vibration changes, so does the cones acceleration. It could be construed that it is the acceleration, or it magnitude, that is responsible for generating the SPL, but this is not the case. The acceleration and frequency determine the peak cone velocity. Acceleration and frequency can change and not change the SPL, but if the peak cone velocity changes, the SPL will change.
The relative size of the cone WRT the wavelength will affect the SPL, but that is mainly a function of dispersion of the total acoustic power.
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