Acoustic Wavefront Mapping in Horn Bends
Note: Links are placed in the text to pictures or graphs of the objects being described.
Horn-loaded loudspeakers, and particularly low frequency horn-loaded loudspeakers, are commonly used in applications where large, linear sound outputs are needed such as in sound reinforcement and active noise cancellation. Because low frequency horns can be very large, they are typically ‘folded’ in various ways. This introduces the bends in such a horn as an element that is not typically accounted for in the initial design process. After building a low frequency horn with round bends and experiencing performance which deviated from predictions, the author became interested in investigating possible causes of these deviations, one of which was hypothesized to be the shape of the bends in the horn. To investigate what happens in the bends of a horn, time-waveform measurements were taken at multiple points in a plane down the center of various bend shapes. These measurements were then processed to allow visualization of sound waves of various frequencies propagating through these bends.
To be able to plot a wave progressing through a bend, a time waveform measurement can be recorded at multiple locations. Then the amplitude at each measurement location can be displayed for a given time value to form a mesh which shows the shape of the acoustic wave at that given time. The only difficulty is that all the measurements must be referenced to some common time. This is simply accomplished by using a two-channel computer-based measurement arrangement. The same signal is output to two channels. One of these channels drives an amplifier, which drives a loudspeaker. The loudspeaker converts the electrical signal to an acoustic wave that travels down the horn and through the bend being measured. The sound wave is picked up by a small measurement microphone and is recorded on an input channel by the computer. Simultaneously on the other channel, the same output signal goes directly to another input channel. The signal on this looped channel serves as a reference for when the measurement taken actually occurred. Here is a sample of what the recorded input signals look like. If only a time delay value is desired, this could be taken from corresponding peaks in the waveforms. If, on the other hand, it is desired to later display the wave traveling down around the bend, the complete recorded signal should be retained. The reference signal can be discarded once the beginning of the measured signal is truncated to a standard time relative to the reference signal.
The equipment used to perform the measurements included a personal computer with a low-cost soundcard. The soundcard ran at a sampling rate of 44.1 kHz, which was adequate for the relatively low frequencies being measured. Noise was the only problem that was feared when using this equipment, but it was found to not be an issue; all the measurement taken were relatively free of noise. Software was written in Matlab using the Data Acquisition toolbox to generate, play, record, and process the measurements. The microphone used was a Panasonic WM60AY Ľ inch diameter back electret capsule. This was modified per Siegfried Linkwitz’s instructions to produce a more linear output for a given sound level. Linkwitz measures the noise floor of these capsules to be about 36 dB SPL from 80 Hz to 20 kHz, with a corner frequency around 100 Hz, below which noise increases as the inverse of frequency. The microphone was mounted to a positioning stand that could move in two dimensions. This allowed the microphone to be placed in any desired position in one plane in the horn bend being measured. To amplify the signal from the microphone to an appropriate level for the soundcard to work with, a microphone preamp was built using a Texas Instruments INA103 low noise, low distortion instrumentation amplifier. The loudspeaker used in the horn was a low-cost 10" diameter long-excursion driver.
Below are some more pictures of my testing setup.
Three bend geometries were measured. They are shown in the previous link with the throat section they were attached. The bends were all based on a square, right angle bend. Corner reflectors of two sizes were added to this square bend. The small reflector was sized to approximate a smooth continuation of the horn around the bend. The large reflector was designed to span the complete horn such that if ray-tracing techniques were used, all the sound coming up the throat would be reflected around the corner.
The bends had square cross sections with a width of 8.5 inches. The total length of the horn was 56 inches. This would place the horn’s lowest resonant frequency at 60 Hz. Although it can be seen from the previous figure that the title of ‘horn’ is a bit of a stretch for the geometry built, the envisioned application of this work was for sections of a horn where the expansion is still slow. The geometry actually appears to be more of a transmission line-type enclosure, although without the front radiation from the driver being utilized.
The three bends were all measured at six frequencies to investigate frequency-dependent effects of the various geometries. These frequencies were 40 Hz, 70 Hz, 175 Hz, 300 Hz, 850 Hz, and 1570 Hz. 40 Hz falls below the lowest resonant frequency of the horn, 70 Hz was chosen for being just above this frequency, and 1570 Hz was used because its wavelength is equal to the width of the bend. The other frequencies fell in between these two ranges and were picked to not fall at frequencies were a resonance occurred due to cone breakup or other effects.
Results are shown here in two different ways. In the first way, results are only shown for 1570 Hz. A sample of these results is shown here. In this view, the bend is on its side, with the center plane where measurements were taken being outlined in black. A sound wave created by the driver will enter the horn on the left, while on the right is the exit of the bend into the room. Each node in the mesh displayed inside the bend is a point where a measurement was taken, each node being 0.5 inches apart. If a given node is above the plane outlined in black, it represents a positive pressure while a node below the plane represents a negative pressure. All the nodes in a given view are plotted at the same time relative to the original reference signal, so a wave can be observed as it moves down the horn.
These animations are .avi files zipped to reduce downloading time.
1570hz animation, square bend - 1.45MB
1570hz animation, small angle bend - 0.94MB
1570hz animation, large angle bend - 0.85MB
Results were also generated by plotting a shaded surface with the color representing the pressure at a given point. These results are shown at 175Hz, 850Hz and 1570Hz. Using standard matlab functions, the shading was set up to be interpolated between measured points. The orientation is as shown in a previous figure, with the entrance of the bend being at the bottom and the exit of the bend to the room at the right.
These animations are .avi files zipped to reduce downloading time.
175Hz animation, square bend - 1.20MB
850Hz animation, square bend - 1.22MB
1570Hz animation, square bend - 1.62MB
175Hz animation, small angle bend - 1.20MB
850Hz animation, small angle bend - 1.32MB
1570Hz animation, small angle bend - 1.39MB
175Hz animation, large angle bend - 1.09MB
850Hz animation, large angle bend - 1.53MB
1570Hz animation, large angle bend - 1.37MB
In general, you may draw your own conclusions from the data presented. The only things I wish to point out are that some of the results may be confusing because of a lack of an appropriate termination to the horn (larger mouth). This is why some of the waves in the shaded animations appear to never leave the horn - the level at the exit is much lower than further back in the horn. Also, some behaviors of the wave are hard to see in the shaded animations, such as the wave reflecting back down the throat of the horn. This is part of why I have both types of representations of the data.
Copyright 1999-2004, John H Sheerin
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