# Measuring sound...with a phone?

Kevin J. Farrell, Principal Engineer, Computational Simulation & Validation

Sound propagates as pressure fluctuates in fluids; measuring sound means converting these fluctuations into electrical signals with a transducer. A sound level meter—a pressure transducer attached to a voltmeter—has often been used to record noise levels around a heat exchanger experiencing acoustic vibration.

The human ear responds to pressure fluctuations over a range of a million to one. The wide range means that an absolute quantification of the sound pressure level in engineering units is cumbersome.

Instead, sound is measured using a logarithmic decibel (dB) ratio scale. Sound pressure level, $L_{P}$, is defined with respect to the smallest amplitude pressure oscillation (20 microPascals) that the human ear can perceive.

$L_{P}=10\textup{log}_{10}\left [ \frac{P}{20\left ( 10^{-6}\right )\textup{Pa}} \right ]^{2}=20\textup{log}_{10}\left [ \frac{P}{20\left ( 10^{-6}\right )\textup{Pa}} \right ]$

Sound power level, $L_{W}$, is also used to quantify a noise source, although it is not directly measurable like the sound pressure level. The reference power in the definition of sound power level is 1 picoWatt.

$L_{W}=10\textup{log}_{10}\left [ \frac{\textup{power}}{\left ( 10^{-12} \right )W} \right ]$

Sometimes engineers use the abbreviation SPL for these measurements. This practice is ambiguous, however, as the $P$ can denote pressure or power. Using actual variables $L_{P}$ or $L_{W}$ is preferred.

To account for the fact that the human ear is not equally sensitive to sound at different frequencies, most industrial sound-level meters incorporate a number of weighting scales (A, B, C, and/or Z). If the meter does not specifically note the weighting scale used, the popular A scale is assumed. As an example of the differences between these scales, the A scale reduces pressure oscillations less than 50 Hz by 30 dB or more whereas the B scale reduces them by about half as much (~15 dB). When sound pressure level measurements are recorded, subscripting the unit or level with the weighting scale (e.g., $dB_{A}$ or $L_{P_{A}}$) is good practice.

Today, smartphones can measure sound levels and complete digital processing tasks. Users can choose different weighting scales and frequency bandwidths to display spectra with peak markers (Figure 1) or easy-to-read waterfall plots (Figure 2). These instruments record the signal in dB relative to full scale, which means the vertical axes on both figures record $20\textup{log}_{10}\left ( \frac{\textup{microphone voltage}}{\textup{maximum microphone voltage}} \right )$, which has a maximum value of zero. The microphone voltage is proportional to the fluctuating pressure amplitude in the acoustic wave. A transducer calibration is required to relate the microphone voltage to an actual acoustic pressure.

Audio recordings can be an invaluable part of HTRI’s analysis. In several instances of troubleshooting a flow-induced vibration (FIV) problem, we have used a simple sound recording made with a client’s cell phone. This allows for a fast Fourier transform of the time trace and confirms peak vibration energy in the spectrum at the tube natural frequency indicated by Xist®.

Technology advancements have greatly assisted our analysis of FIV problems. Measurements from affordable and readily available sensors and CFD simulation of flows have been instrumental in understanding and mitigating FIV problems in many types of process heat exchangers.

One tool to gather valuable evidence could already be in your hands!