Calculating Work Done by Speaker Cone at 40Hz

[tfowler306]

we measure amplifier output in watts, and speakers in db spl which is logrimithic to the power applied, so if I have a 4 ohm speaker that will create 91 db of spl when 2.83v is applied how much work is done?

Watts = V^2/R = W=2.83^2/4 = W=8/4 so W= 2 this is the power applied to the speaker if I want to know the force applied to the speaker cone (f=ma) the moving mass with air load for the speaker is 142.7grams, how do I find the acceleration of the speaker cone? If the speaker is producing a steady frequency let's say 40Hz it would have no acceleration it would be a constant velocity. I am stumped on where to go for this one...

 

[russ_watters]

The speaker cone certainly accelerates - the frequency of 40 hz means it is vibrating back and forth 40 times a second. Ideally, it should vibrate a distance equal to the wavelength, but at low frequencies, it probably can't move far enough. You can calculate the distance traveled using the speed of sound - it's the wavelength of the sound wave. Then see if it makes sense as a distance. Realistically, a woofer can probably only move an inch or so in and out.

Note that the actual efficiency of sound systems is very low. The amount of energy actually moving through the air is a few percent, at most, of the rating of the amplifier.

 

[rcgldr]

Wiki links:

http://en.wikipedia.org/wiki/Loudspeaker

http://en.wikipedia.org/wiki/Sound_power_level

http://en.wikipedia.org/wiki/Sound_pressure_level

Generally, better speakers have more negative feedback, acoustical (sealed) and/or electrical dampening. Most of this dampening is to prevent overshoot as with any servo system. Also although the inner diaphram of a speaker moves back in forth in sync with the signal, the speaker itself ends up with wave patterns, with usually moving peaks and valleys, although the entire speaker moves a lot at lower frequencies.

So the efficiency of speakers is pretty low (about 1/2%), and lower still for high quality sounding speakers. Power output is a fraction of power consumed, especially with musically oriented (as opposed to home theater) speakers.

 

[tfowler306]

the wave length of a 20Khz signal is in the 150 meeter band, so the speaker cone can't move to the length of the sound wave. That in itself is confusing to me, because a tweeter cone on average will only move 0.03 mm. but from what you said it gives me a direction on how to calculat the average velocity of the cone frome the Thele Small perameters. The current speaker has a 7/16" max excursion and a motor force of 13.93 Tm at 750W. so from there I can figure out the excursion at 2W and that is the total distance traveled back and forth at 40times/secdevided by 2 because a sinwave is from 0 to 0 which actually would equal a velocity of 0 because there is no displacement, but for one full stroke of the speaker I can have a velocity for that period of the stroke

does this make sense?

 

[rcgldr]

The current speaker has a 7/16" max excursion and a motor force of 13.93 Tm at 750W.

Only the pole piece (see wiki article) moves directly in response to the signal received. The diaphram (see wiki article) ends up with multiple peaks and valleys that actually produce the sound. Even at a single fixed frequency, these peaks and valleys will move around unless there is some harmonic relationship between the diaphram and the input signal.