6.7. Frequency–response curves

A frequency–response curve of a loudspeaker is defined as the variation in sound pressure or acoustic power as a function of frequency, with some quantity such as voltage or electrical power held constant. To calculate the full frequency response, we refer to Fig. 6.4 but using Eqs. (13.116)–(13.118) for the exact acoustic radiation impedance instead of lumped elements. The total impedance in the loop with all quantities referred to the mechanical side is
ZMT=B2l2Rg+RE+jωLE+jωMMD+RMS+1jωCMS+2SDρ0c(1J1(2ka)ka+jH1(2ka)ka)
image (6.41)
where k   =   ω/c. The diaphragm velocity is then given by the driving force divided by the total impedance
uc(rms)=|eg(rms)Bl(Rg+RE+jωLE)ZMT|
image (6.42)
We than calculate the on-axis pressure using
prms(r)=ρ0fSDuc(rms)r
image (6.43)
and
SPL=20log10(prms(r)pref)
image (6.44)
where p ref   =   20   μPa rms. The on-axis pressure of a typical 100   mm loudspeaker in an infinite baffle is plotted in Fig. 6.7. For this application, the mass of the cone is made as light as possible and the compliance of the suspension as high as possible consistent with mechanical stability. The high frequency response is aided by means of a concentric secondary or “whizzer” cone.
image
Figure 6.7 On-axis pressure response and efficiency of an electrodynamic loudspeaker in an infinite baffle for which e g(rms)   =   2.83 Vrms, R E   =   7   Ω, L E   =   100   μH, Q ES   =   2.2, Q MS   =   5, f S   =   125   Hz, S D   =   56   cm2, and V AS   =   2   L.
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