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arxiv: 1906.08778 · v1 · pith:KMIGU72Enew · submitted 2019-06-20 · ⚛️ physics.ed-ph · physics.ins-det

Low-cost ultrasonic distance measurement in a mechanical resonance experiment

William D. Joysey , Axel Mellinger This is my paper

Pith reviewed 2026-05-25 18:53 UTC · model grok-4.3

classification ⚛️ physics.ed-ph physics.ins-det
keywords ultrasonic sensorsmechanical resonancedamped oscillatorlow-cost instrumentationSavitzky-Golay filterphysics laboratoryESP8266 microcontrollerdata acquisition
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The pith

Low-cost ultrasonic sensors with lag compensation enable resonance curve measurements in student labs.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents a low-cost dual-probe position sensor system for a mechanical resonance experiment. It uses US-100 ultrasonic distance sensors paired with ESP8266 microcontrollers to record the motion of a driven, damped spring oscillator. A modified Savitzky-Golay filter compensates for sensor lag, and data is transferred via Wi-Fi for analysis in Logger Pro. This setup allows students in large lab courses to collect sufficient data to plot amplitude and phase lag as functions of driving frequency.

Core claim

The authors demonstrate that the position of the two ends of a driven damped spring oscillator can be measured using inexpensive ultrasonic sensors and microcontrollers, with a modified Savitzky-Golay filter to correct for sensor response lag, enabling the acquisition and wireless transfer of data suitable for generating resonance curves in an educational setting.

What carries the argument

The modified Savitzky-Golay filter that compensates for sensor lag in the ultrasonic position measurements.

Load-bearing premise

The ultrasonic sensors and lag compensation provide position data accurate enough for students to plot reliable amplitude and phase lag curves as a function of driving frequency.

What would settle it

Measuring the same resonance experiment with a calibrated high-precision position sensor and comparing the resulting amplitude and phase curves would test whether the low-cost system yields equivalent results.

Figures

Figures reproduced from arXiv: 1906.08778 by Axel Mellinger, William D. Joysey.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic view of the apparatus for apparatus for [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Wiring schematics of the ESP8266-based WeMos D1 [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Ultrasonic sensor head with its 3D-printed enclosure. [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Web interface of the ESP8266 microcontroller, show [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Amplitude ratio [PITH_FULL_IMAGE:figures/full_fig_p004_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Phase lag vs. driving frequency, with and without the [PITH_FULL_IMAGE:figures/full_fig_p004_9.png] view at source ↗
read the original abstract

We present a low-cost, dual-probe position sensor in a mechanical resonance experiment suitable for deployment in large lab courses with multiple stations. The motion of the two ends of a driven, damped spring oscillator is recorded with US-100 ultrasonic distance sensors and ESP8266 microcontrollers. Sensor lag is compensated via a modified Savitzky-Golay filter. Data is downloaded to a computer via Wi-Fi in a format suitable for analysis in Logger Pro. Due to the simple and fast data acquisition process, students can gather sufficient data to plot curves of the amplitude and phase lag as a function of driving frequency.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript describes a low-cost dual-probe ultrasonic position measurement system for a mechanical resonance experiment. It uses US-100 sensors paired with ESP8266 microcontrollers to record motion at both ends of a driven, damped spring oscillator, applies a modified Savitzky-Golay filter to compensate for sensor lag, and transfers data via Wi-Fi to a computer for analysis in Logger Pro. The goal is to enable students in large lab courses to collect sufficient data for plotting amplitude and phase lag versus driving frequency.

Significance. If the residual errors after lag compensation prove negligible for the target measurements, the setup would offer a practical, inexpensive alternative to commercial sensors, supporting scalable hands-on resonance experiments without requiring expensive equipment per station.

major comments (2)
  1. The central pedagogical claim—that the US-100 + ESP8266 system with the described filter yields position time series accurate enough for students to extract reliable amplitude and phase-vs-frequency curves—is unsupported by any validation data, error analysis, or comparison against a reference instrument. This absence is load-bearing because the manuscript supplies no quantitative demonstration that residual lag or measurement uncertainty remains below the threshold needed for the intended student analysis.
  2. No assessment is provided of potential systematic effects such as acoustic crosstalk between the two co-located ultrasonic sensors, temperature dependence of sound speed, or range limitations of the US-100 at the amplitudes typical of the resonance experiment. These factors directly affect whether the dual-probe configuration can deliver independent, accurate traces at both ends of the oscillator.
minor comments (2)
  1. The description of the modified Savitzky-Golay filter would benefit from an explicit statement of the window size, polynomial order, and the precise lag-compensation step (e.g., forward prediction or time-shift adjustment) so that readers can reproduce the correction.
  2. A parts list with current prices and a wiring diagram (even if schematic) would improve reproducibility for instructors setting up multiple stations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address each major comment below and will revise the manuscript accordingly to strengthen the validation of the sensor system.

read point-by-point responses

  1. Referee: The central pedagogical claim—that the US-100 + ESP8266 system with the described filter yields position time series accurate enough for students to extract reliable amplitude and phase-vs-frequency curves—is unsupported by any validation data, error analysis, or comparison against a reference instrument. This absence is load-bearing because the manuscript supplies no quantitative demonstration that residual lag or measurement uncertainty remains below the threshold needed for the intended student analysis.

    Authors: We acknowledge that the manuscript does not include direct validation against a reference instrument or quantitative error bounds on residual lag after compensation. To address this, the revised manuscript will add a new section presenting comparisons of US-100 measurements to a calibrated linear potentiometer over multiple oscillation cycles, along with an error analysis (RMS deviation and phase uncertainty) demonstrating that residuals remain below the level needed for reliable student extraction of amplitude and phase curves. revision: yes

  2. Referee: No assessment is provided of potential systematic effects such as acoustic crosstalk between the two co-located ultrasonic sensors, temperature dependence of sound speed, or range limitations of the US-100 at the amplitudes typical of the resonance experiment. These factors directly affect whether the dual-probe configuration can deliver independent, accurate traces at both ends of the oscillator.

    Authors: We agree these systematic effects require explicit assessment. The revised manuscript will include new measurements and discussion of (i) acoustic crosstalk by comparing single-sensor vs. dual-sensor operation, (ii) temperature dependence via controlled calibration runs, and (iii) range limitations tested across the amplitude range used in the resonance experiment. These will be shown to be either negligible or correctable within the experimental protocol. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The manuscript is an instrumentation note describing a low-cost ultrasonic sensor setup with ESP8266 microcontrollers and a modified Savitzky-Golay filter for lag compensation in a driven spring oscillator. It supplies parts lists, wiring, filter details, and data export format but contains no derivations, predictions, fitted parameters presented as results, or load-bearing self-citations. The central claim is pedagogical feasibility of the hardware chain, which rests on explicit implementation choices rather than any reduction to its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No free parameters, axioms, or invented entities; the work is a description of an off-the-shelf hardware integration for teaching.

pith-pipeline@v0.9.0 · 5622 in / 935 out tokens · 18904 ms · 2026-05-25T18:53:53.960741+00:00 · methodology

discussion (0)

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Reference graph

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