Violin vibration and acoustics

Research question

As a violinist, I wanted to understand how differences in an instrument’s structure appear in its vibration and sound. My master’s thesis compared a 2019 William Bagnato violin and a 2021 Franz Hoffman Vienna violin using accelerometers, a modal hammer, and a measurement microphone.

I examined the harmonic response of the top plate, the response near the bridge, and the sound radiated into an anechoic room. I also worked to control differences in strings and accessories so the comparison focused more directly on the instruments’ wooden bodies.

Mapping the vibrating surface

I defined 67 accelerometer locations across each top plate, including the perimeter, the central region, and points near the bridge. For the string-excitation measurements, I recorded three runs at each point and compared spatial averages for the whole plate, its top, middle, and bottom regions, and its edges.

The 67 accelerometer positions marked across the violin top plate — The 67-point measurement map used for string-excitation tests. Thesis Figure 5.10.

Accelerometer placement on the top plate near the bridge.

Recording the instrument’s dimensions with digital calipers.

For bridge excitation, I applied the modal hammer at the top center of the bridge and measured four surrounding points. This gave a complementary view of the body’s response to an impact, alongside the harmonic response generated by plucking the G and E strings.

Data acquisition and signal processing

I built a LabVIEW acquisition program to display sensor signals and calculate frequency spectra. The setup used a National Instruments 9234 module with integrated signal conditioning and anti-aliasing filters; the recorded spectra were organized for comparison and spatial averaging.

Excitation consistency was part of the experiment. I kept the string-plucking location fixed, checked the plucking motion with an accelerometer on the pick, and screened hammer strikes for misses and large force differences.

Data acquisition interface with acceleration, force and FFT plots — The acquisition interface displays acceleration, hammer input, and the transformed frequency response.

Vibration results

The string-excitation spectra show how harmonic amplitudes vary between the two instruments. Spatial averaging made it possible to compare the full top plate while also examining where particular frequency components were strongest.

Four spectra comparing spatially averaged G-string and E-string vibration in the two violins — Spatially averaged top-plate vibration under string excitation. Original thesis Figure 7.1; the panels retain their original axis scales.

Bridge-excitation accelerometer spectra for the two tested violins — Spatially averaged accelerometer responses of the two violins under bridge excitation. Each panel shows its own amplitude scale.

In this pair of instruments, the Bagnato violin showed stronger lower-frequency harmonic response in the middle region of the top plate. The bridge-impact measurements also showed different distributions of response peaks, linking the comparison to both excitation method and measurement location.

Acoustic measurements

I recorded the plucked-string response in CSULB’s anechoic chamber, with the microphone positioned 3 feet 3 inches above the top plate. Foam support, microphone placement, and equipment positioning were chosen to keep the measurement conditions consistent.

Violin supported with measurement equipment in an anechoic room — The anechoic-room setup used for the experimental work.

Microphone spectra comparing the two violins under G-string and E-string excitation — Radiated sound measured in the anechoic chamber. Original thesis Figure 7.10.

I compared the microphone spectra with the accelerometer measurements and examined the balance of lower and higher harmonics. The thesis interprets these results using equal-loudness contours, relating the measured differences to the tonal character of the two instruments.

Master’s thesis

Structural Properties and Perceived Acoustic Quality of Modern Violins.
Alan Pham. MS in Mechanical Engineering, California State University, Long Beach, May 2022.

The complete thesis includes the experimental design, instrumentation, signal-processing methods, measurement maps, and vibration and acoustic results.

Read the complete thesis (PDF) ↗ProQuest record ↗

Thesis committee: Jalal Torabzadeh (chair), Allen Teagle, and Emel Demircan.

Alan Pham playing violin — Playing violin in 2025. My musical experience continues alongside my engineering research.