Introduction:

Following from last homework I will continue to evaluate the “goodness” of my new speakers.

A key consideration when designing a speaker is the lobbing effect. Lobbing is essentially the interference pattern caused when two or more acoustic transducers produce a sound wave. As those waves radiate out they will interfere with one another - and hence the lobbing interference pattern. There are several attributes, both mechanically and electrically, that define a lobbing pattern - but here I will ignore the theory and just graph some data.

Typically lobbing is expressed at a given frequency - I however was interested in the sound pressure level radiation pattern. In particular how my room acoustic added to the interference pattern.

Data Collection:

The Python files in this repo were used to gather the data. The procedure was as follows:

  1. Place the microphone 1m away from the center of the speaker at {-45°, -30°, -15°, 0°, 15°, 30°, 45°} off axis both horizontally and vertically for a total of 49 listening positions
  2. For each listening position record 30 0.1 second samples of white-noise (uniform power density 20Hz-20kHz)
  3. Perform an FFT on each of the 30 samples per listening positions and average the FFTs
  4. With an averages FFT calculate the total power of the waveform captured converting to watts
  5. Convert wattage to SPL using manufacture provided speaker efficiency

The white-noise and all samples were played/recorded at 44.1kHz 16bit with no compression.

R Code

library(plotly)
## Loading required package: ggplot2
## 
## Attaching package: 'plotly'
## The following object is masked from 'package:ggplot2':
## 
##     last_plot
## The following object is masked from 'package:stats':
## 
##     filter
## The following object is masked from 'package:graphics':
## 
##     layout
# The supporting Python files do a lot of the heavy lifting for pre-processing the data.

speaker_data = read.csv("/Users/brendo/repos/dynamic-graphs-brendo61-byte/Python/speaker_data.csv")
db_levels = read.csv("/Users/brendo/repos/dynamic-graphs-brendo61-byte/Python/db_levels.csv")
db_levels = matrix(as.numeric(unlist(db_levels)),nrow=nrow(db_levels))
db_levels = db_levels[, 2:8]

fig <- plot_ly(x = sort(unique(speaker_data$x)), y = sort(unique(speaker_data$y)), z = db_levels) %>% 
  add_surface() %>% 
  layout(scene = list(xaxis=list(title="Horizontal Off Axis (°)"),
                      yaxis=list(title="Vertical Off Axis (°)"),
                      zaxis=list(title="SPL (dB)")),
         title = "Speaker SPL Lobbing Pattern")

fig

Interpreting Results

What was the most impressive was the vertical off axis response; SPL is not affected by vertical angle. Now, as a human with ears I can confidently say the sound changes so perhaps a frequency breakdown is also needed; but from the figure above SPL is only dependent on horizontal angle.

The two valleys at ±15° horizontally are to be expected as this shape is typical of a two-way design; i.e. tweeter and woofer. What is interesting here is that this shape is typical for for a two-way design where the two transducers are vertically stacked - for speaker being testing the transducers are in the same horizontal plane. It stands to reason that the radiation pattern would be rotated 90° and the above figure supports that hypothesis.

If the microphone were to be placed 1 meter from the speaker at 60° it would be in the wall. While in the opposite direction the room opens up. These hard and soft surfaces could highlight the non symmetric nature across the horizontal plane.