Changes in Location and Intensity of Impulse on a Snare Drum Class: Applied Acoustics Professor: Peter Zhang
Written By John Garretson
Additional Group Members: Timothy Rimnac Zach Wagner Daniel Kahn
Abstract A Gretch snare drumâ€™s impulse response was analyzed to determine the effect of changes in location and intensity of impulse. The drum was struck with three different intensities at every position, and a total of nine different positions were used that ran across the diameter of the drum. Results indicate that the second harmonic becomes more dominant in the frequency response as both intensity of impulse and the distance from impulse location to the center of the drum increase.
1. Introduction Zach Wagner, Daniel Kahn, Timothy Rimnac, and John Garretson performed an experiment on a snare drum at Columbia College of Chicago October 27th 2010 to analyze changes in intensity and location of impulse on frequency response.
2. Methods A Gretsch Catalina Maple snare drum was tested by making wave recordings of the drum being hit at nine different locations across the drumâ€™s diameter. At each location a recording was made of the drum being struck at three different intensities, light, medium, and hard. The spectrum of each recording was visually analyzed to find trends using SpectraPlus signal analyzing software. A diagram of the locations can be seen below in Figure 1.
Figure 1 Approximation of nine locations of impulse.
3. Results Waterfall representations from SpectraPlus can be seen in the following in Figures 2-10. Figure 10 is the center position and Figures 2-9 are the equal radius pairs. Analyzing the spectrum of the recordings showed that at all locations and impulse intensity combinations the highest peaks in the frequency response are at 192Hz and 279Hz approximately, with the rest of the spectrums harmonics remaining very similar, but showing the same relative relationship as 192Hz and 279Hz. This can be seen in Figure 2 as well as Figures 3-Figure11. Changes in location and impulse intensity determined which of the two frequencies had the highest
peak. The easiest trend to see in the data was that as intensity increased the level of all frequencies also increased. Other trends in the frequency domains of the recordings showed that the closer to the Center position the impulse took place the stronger the 192 Hz band over the 279 Hz band, and as the position got farther from the center the more prominent the 279Hz band gets and the 192Hz band falls off. This can be seen by observing the relationship between the levels of the 192Hz peak and the 279Hz peak in the light and medium impulse responses as the position gets farther from the center. The data also shows that as the intensity of the impulse is increased the 279Hz band becomes more prominent. This can be seen in Figures 2-5 by comparing the relationship of the 192Hz and 279Hz bands in the hardest impulse response of each graph to the lightest and medium impulse. The 192Hz band is larger for the softer impulses, because it is close to the center, but the hard impulse responses near the center show that the 279Hz is more prominent.
3.1 Pair 1 X.1
Figure 3 Waterfall representation of frequency domain at position 1.1.
Figure 4 Waterfall representation of frequency domain at position 2.1
Figure 2 The relatively identical frequencies for harmonics over all intensities and locations.
3.2 Pair 2 X.2
3.3 Pair 3 X.3
Figure 5 Waterfall representation of frequency domain at position 2.2.
Figure 7 Waterfall representation of frequency domain at position 2.3.
Figure 6 Waterfall representation of frequency domain at position 1.2.
Figure 8 Waterfall representation of frequency domain at position 1.3
3.4 Pair 4 X.4
Figure 9 Waterfall representation of frequency domain at position 2.4.
4. Discussion The locations and intensity of the impulse responses were not documented in more detail because of a lack of total precision due to the human element of the impulse. More accurate and useful data could be acquired by controlling the exact locations of the impulses as well as having a more reproducible force for each of the three intensity levels. Also, if further experiments were done using a different diameter I would expect similar results with the relationships between intensity and location of impulse and the frequency response of the drum. Errors can be attributed to the lack precision within location and intensity variables as well as the restraints of the SpectraPlus user interface that restrict more accurate measurements.
Figure 10 Waterfall representation of frequency domain at position 1.4
Figure 11 Waterfall representation of frequency domain at Center position.
In conclusion, the data suggests that as intensity of and impulse increases and as the location of an impulse gets farther from the center of a snare drum the most prominent spectral element shifts from its first harmonic to its second harmonic with later harmonics showing the influence of this relationship as well.