Cyklop
13 november 2011
· 1 277 Inlägg
The results of these measurements are shown in Figure 2.2. The top plot is the
magnitude and phase of the system impedance. The middle plot is the SPL and phase
of the woofer response. The bottom plot is the SPL and phase of the terminus response.
Each plot contains a title describing the measurement being presented. Each plot also
contains the sampling rate and sample size used during the measurement. For all of the
frequency response plots, ten measurements were averaged to get the final data.
The measurements were repeated after stuffing the tube with 100 gm, 200 gm,
and 300 gm of Dacron Hollofil II fiber. To stuff the tube, I made a 48” long cheese-cloth
cylinder and tied the ends closed with string. To add or remove stuffing, the cheese-cloth
cylinder was pulled out of the cardboard tube, untied, and unrolled flat. This technique
made it easy to adjust the amount and type of stuffing in the test transmission line.
Figures 2.3, 2.4, and 2.5 show the results of the measurements for 100 gm, 200 gm, and
300 gm of Dacron Hollofil II stuffing. The format of the plots is the same as described for
Figure 2.2.
I studied the measurement results to try and understand the behavior of the test
transmission line. I started with the unstuffed measurements shown in Figure 2.2. A lot
can be learned from these three plots. First, I calculated the quarter wavelength modes
of the tube after including an end correction to the tube length corresponding to an
unflanged exit boundary condition. The ¼ wavelength calculation is shown below.
Ltube = 48.25” = 1.226 m
Leffective = 48.25” + 0.6 x 3.625” = 1.281 m
f = c / (4 Leffective) = 67 Hz
cair = 342 m/sec
Table 2.2 shows the driver resonant frequency, the calculated tube quarter wavelength
frequencies, and the measured system peaks from the plots in Figure 2.2.
Table 2.2 : Calculated and Measured Frequencies for the Unstuffed Test Line
Mode Measured Driver
Resonance (Hz)
Calculated Tube
Frequencies (Hz)
Measured System
Frequencies (Hz)
Driver 34 22
1/4 Wavelength 67 94
3/4 Wavelength 200 214
5/4 Wavelength 334 343
7/4 Wavelength 467 475
9/4 Wavelength 601 598
11/4 Wavelength 734 727
The first thing I noticed in Figure 2.2 was a shift of the driver resonant frequency
in the impedance curve. The driver resonant frequency of approximately 34 Hz, as
reported in Table 2.1, dropped to 22 Hz when the driver was mounted in the test
transmission line. I attribute this change in frequency to an additional mass loading on
the speaker cone from the air moving in the transmission line. At this low frequency, the
air in the transmission line acts like a solid slug of mass. Using the value of Mmd from
Table 2.1 and the mass of air in the tube, the lowest system resonant frequency can be
estimated and compared to the measured value.
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