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

15.14. Setting tension to limit displacement and maintain stability

The stress must not exceed the maximum value σ _max for the membrane material, which for polyester is 55–75 MPa, yet for stability it must be greater than the minimum value given by Eq. (15.74). Hence the tension should lie within the range

\frac{2 ε_{0} a^{2}}{α_{0}^{2} d} {(\frac{E_{P}}{d})}^{2} < T < σ_{\max} h,

$\frac{2 ε_{0} a^{2}}{α_{0}^{2} d} {(\frac{E_{P}}{d})}^{2} < T < σ_{\max} h,$

(15.84)

where h is the thickness of the membrane. However, the tension is usually set to at least three times the minimum value for stability to allow for varying environmental conditions and aging. Now that we have established the safe limits for the tension, we wish to set it so that the displacement at low frequencies stays within the gap width d. By applying ohms law to the total impedance of the two compliant elements, C _MD0 and − C _ME0, given by Eqs. (15.77) and (15.78) respectively and shown in Fig. 15.17, then rearranging we obtain

T = \frac{4 C_{E} E_{P}}{π α_{0}^{2} d} (\frac{2 {\tilde{e}}_{in}}{α_{0}^{2} {\tilde{η}}_{a v}} + \frac{E_{P}}{d}) .

$T = \frac{4 C_{E} E_{P}}{π α_{0}^{2} d} (\frac{2 {\tilde{e}}_{in}}{α_{0}^{2} {\tilde{η}}_{a v}} + \frac{E_{P}}{d}) .$

(15.85)

The most efficient way to operate the loudspeaker is to arrange for the maximum peak input voltage to be equal to twice the polarization voltage. Also, let us set the peak average displacement to one-third of the gap width so that