Which dB @1M/1Watt Constitutes 100% Efficiency?

[kelticwizard]

Friend has a pair of old Cerwin Vega PD-3 PA speakers which need midranges-not just diaphragms, there is a hole where the midranges used to be.

Found out the midrange on this model is the Cerwin Vega H25.

Looking at the frequency response, which I found here, I noticed that this unit seems to be putting out 112 dB @ 1M/1Watt.

Chart is reproduced below.

Win ISD will not allow simulations above 106 dB at 1M/1 Watt.

Small's chart for bass response tops out at 112 dB at 1M/1 Watt.


Seems to me this chart shows the Cerwin Vega, through part of it's band, as being either 100% efficient or 400% efficient, 6 dB meaning 4 times the power. Even 100% efficiency seems far fetched, 50% efficiency is superb.

Any help understanding this would be appreciated.

[Cal Weldon]

KW,

According to this calculator 112dB at 1 watt translates to an efficiency rating of 1 or 100%

http://www.sengpielaudio.com/calculator-efficiency.htm

[454Casull]

Omnipolar radiation?

[poptart]

that's impossible, nothing is 100% efficient. I didn't think speakers were even close...?

[Cloth Ears]

Wiki. Theoretically, if you have a driver with Fs of 116Hz, Vas of 403 litres and Qes of 0.6, then you'll have a 100% efficient driver (ie. 112dB/1w/1m).

But, nature will conspire against you to ensure that this (or other) set(s) of combinations for your driver will not occur.

[Cal Weldon]

Originally posted by 454Casull
Omnipolar radiation?

No, 1W, 1M, on axis

[Rybaudio]

This is dependent upon the radiation pattern of the device. Remember, when you measure 112 dB you are measuring the intensity (power per unit area) at that point, not the power being radiated by the device. The reference intensity I_o is 10^-12 watts/m^2, and SPL is given by

SPL = 10*log(I/I_o) = 120 + 10*log(I)

so if you have 1 watt of full space radiation you get

SPL = 120 + 10*log( 1w / 4pi ) = 109

or in half space you get

SPL = 120 + 10*log( 1w / 2pi ) = 112

If, for a rough approximation, you treat the device as if it has uniform axisymmetric radiation with an exact beamwidth of x degrees, then the area radiated over at 1 m is 2*pi*(1 - cos(x/2)) so the SPL for 1 watt of radiation is:

SPL = 120 + 10*log(1 / 2*pi*(1 - cos(x/2)) ) = 120 - 10log(2pi) - 10*log(1 - cos(x/2)) = 112 - 10*log(1 - cos(x/2))

A couple sample values:

BW SPL
360 109
180 112
120 115
90 117.3
60 120.7

I hope this helps

Nolen

[Conrad Hoffman]

Rybaudio- I started to do the same calc, but got lost right at the beginning. How do you get from the 0dB level of 0.0002 dynes/cm^2 to watts/cm^2? There's something really simple I'm missing!

[mzzj]

Originally posted by Conrad Hoffman
Rybaudio- I started to do the same calc, but got lost right at the beginning. How do you get from the 0dB level of 0.0002 dynes/cm^2 to watts/cm^2? There's something really simple I'm missing!

I guess that Rybaudio was using approxmate value of 10^-12 W/m2 right away as it is commonly used in calculations like this.

I found following http://en.wikipedia.org/wiki/Sound_power
P=(A*p^2)/Z
Z is the acoustic impedance of air, at +25c about 410 (Pa*s/m)

SPL 0db reference level of 20uPascal translates then to 20u*20u*1m2/410 =0.976pW/m2 which rounds up to easy 10^-12 W/m2

[Rybaudio]

I got that value from a reference textbook a while back and have used it so many times that I just remember it. I think it was in Kinsler and Frey's Fundamentals of Acoustics, but I'm not sure and right now most of my books are packed away in a move.