Acoustics

Search in book...
Toggle Font Controls
Create new playlist

Name your new playlist

Playlist description (optional)
Sign In

Email address

Password

Forgot Password?

or

Continue with Facebook

Continue with Google
Sign Up

Full Name

Email address

Confirm Email Address

Password

or

Continue with Facebook

Continue with Google

6.4. Power output

The acoustic power radiated in watts from both the rear and the front sides of the loudspeaker is

W = {| \frac{{\tilde{u}}_{c}}{\sqrt{2}} |}^{2} (2 R_{M R})

$W = {| \frac{{\tilde{u}}_{c}}{\sqrt{2}} |}^{2} (2 R_{M R})$

(6.19)

Hence, assuming ω ² L ² ≪ (R _g + R _E)², and using Eq. (6.1) for

{\tilde{u}}_{c}

${\tilde{u}}_{c}$

, we obtain

W = {| \frac{{\tilde{e}}_{g}}{\sqrt{2}} |}^{2} \frac{2 B^{2} l^{2} R_{M R}}{{(R_{g} + R_{E})}^{2} (R_{M}^{2} + X_{M}^{2})}

$W = {| \frac{{\tilde{e}}_{g}}{\sqrt{2}} |}^{2} \frac{2 B^{2} l^{2} R_{M R}}{{(R_{g} + R_{E})}^{2} (R_{M}^{2} + X_{M}^{2})}$

(6.20)

Above the suspension resonance frequency, the diaphragm mass dominates so that X _M ≫ R _M where X _M ≈ jωM _MS. In addition, when the wavelength is small compared with the diameter of the diaphragm, we see from Table 4.4 that

R_{M R} = \frac{ω^{2} S_{D}^{2} ρ_{0}}{2 π c}

$R_{M R} = \frac{ω^{2} S_{D}^{2} ρ_{0}}{2 π c}$

(6.21)

where

S_{D} = π a^{2}

$S_{D} = π a^{2}$

(6.22)

is the effective area of the diaphragm of Fig. 6.1. Inserting these into Eq. (6.20) yields

W = \frac{e_{g (rms)}^{2} B^{2} l^{2} S_{D}^{2} ρ_{0}}{π {(R_{g} + R_{E})}^{2} M_{M S}^{2} c}, 2 f_{0} < f < \frac{c}{4 π a}

$W = \frac{e_{g (rms)}^{2} B^{2} l^{2} S_{D}^{2} ρ_{0}}{π {(R_{g} + R_{E})}^{2} M_{M S}^{2} c}, 2 f_{0} < f < \frac{c}{4 π a}$

(6.23)

where

e_{g (rms)} = | \frac{{\tilde{e}}_{g}}{\sqrt{2}} |

$e_{g (rms)} = | \frac{{\tilde{e}}_{g}}{\sqrt{2}} |$

(6.24)

In this frequency range, the radiated power is fairly constant because, as the frequency increases, the falling velocity is compensated for by the rising radiation resistance. At higher frequencies where R _MR = S _D ρ ₀ c, we have

W = \frac{2 e_{g (rms)}^{2} B^{2} l^{2} S_{D} ρ_{0} c}{{(R_{g} + R_{E})}^{2} ω^{2} M_{M S}^{2}}, f > \frac{5 c}{2 π a}

$W = \frac{2 e_{g (rms)}^{2} B^{2} l^{2} S_{D} ρ_{0} c}{{(R_{g} + R_{E})}^{2} ω^{2} M_{M S}^{2}}, f > \frac{5 c}{2 π a}$

(6.25)

Hence, the radiated power is proportional to the inverse square of the frequency when the radiation impedance is mainly resistive and the equivalent circuit is that shown in Fig. 6.6d.

..................Content has been hidden....................

You can't read the all page of ebook, please click here login for view all page.

Table of Contents for Acoustics

Create new playlist

Sign In

Sign Up

6.4. Power output

Table of Contents for
Acoustics