Sound waves are wave phenomena that travel at a speed of approximately 340 meters per second. We hear these waves as they travel through the air. These waves are generated by continuous pressure fluctuations (alternating pressure changes) in the atmospheric pressure of the air.
A sound level meter is a measuring instrument that can measure sound pressure levels. The microphone in the sound level meter converts fluctuations in this pressure (instantaneous sound pressure) into an electrical signal. The sound level meter itself performs several calculations based on this instantaneous sound pressure to calculate the sound pressure level.
This measurement column will introduce an example of recording a WAVE file using the sound recording function of a sound level meter and then calculating the noise level (A-weighted sound pressure level) from it using Microsoft Excel. We hope this will deepen your understanding of the calculation processes performed inside the sound level meter and how it works.
Example of a measurement system
- ONO SOKKI LA-3560 Precision Sound Level Meter
(Configuration: LA-0354 Sound Recording Function) - ONO SOKKI Time Series Data Analysis Tool Oscope 2
(Configuration: OS-2600 Standard) - Microsoft Office Excel 2003
Measuring the sound of hitting a "coffee can (empty can)".
Figure 1 shows a portion of the Excel file (emm131-can.xls) used to calculate the A-weighted sound pressure level from the sound of striking a "coffee can (empty can)".
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Figure 1: Calculation of A-weighted sound pressure level from the sound of striking a "coffee can (empty can)".
Columns A and B contain data obtained by exporting 1 second of data from a WAVE file recorded using the sound recording function of the LA-3560 sound level meter to a CSV file using Oscope2, and then importing it into Excel. Column A shows the time, and Column B shows the instantaneous sound pressure [Pa].
The data in column C (instantaneous sound pressure (A)) is obtained by applying an A-weighting filter to the data in column B (instantaneous sound pressure). Column C contains the formula for calculating the A-weighting filter (6th-order IIR filter). For example, cell C15 contains the following formula:
=($J$14*B15+$J$13*B14+$J$12*B13+$J$11*B12+$J$10*B11+$J$9*B10+$J$8*B9)-
($H$13*C14+$H$12*C13+$H$11*C12+$H$10*C11+$H$9*C10+$H$8*C9)
The data in column D (the squared value of instantaneous sound pressure (A)) is the squared value of the data in column C.
In column E, dynamic characteristics (Fast: 125ms, Slow: 1s, etc.) are applied, and calculations equivalent to a dynamic characteristic circuit (a smoothing circuit using resistors and capacitors) are performed to obtain the mean square [Pa²] (square of the effective value). This result corresponds to the square of the sound pressure. For example, the following formula is entered in cell E15.
=E14+$H$6*(D15-E14)
Here, the value of cell $H$6 is a constant called h0, and the value of h0 is determined by the sampling frequency and the dynamic characteristics (time constant).
The data in column F (A-weighted sound pressure level) is calculated as sound pressure level [dB] from the square of the sound pressure. In this case, the reference sound pressure level used is P0 = 20 μPa.
Figures 2 and 3 show graphs of instantaneous sound pressure, instantaneous sound pressure (A-weighted), and A-weighted sound pressure level. The horizontal axis of the graphs represents 1 second. Figure 2 shows the dynamic response Fast (125 ms), and Figure 3 shows the dynamic response 10 ms.
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Figure 2 shows the instantaneous sound pressure, instantaneous sound pressure (A-weighted), and A-weighted sound pressure level (dynamic characteristic Fast) for a "coffee can (empty can)".
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Figure 3 shows the instantaneous sound pressure, instantaneous sound pressure (A-weighted), and A-weighted sound pressure level (dynamic response 10 ms) of a "coffee can (empty can)".
The maximum sound pressure level is 79.6 dB for the Fast dynamic response (125 ms), but 87.4 dB for the 10 ms dynamic response, showing that the shorter the dynamic response (time constant), the higher the sound pressure level. This is because a longer time constant smooths out rapid changes. Generally, when evaluating the magnitude of an impact sound by its maximum sound pressure level, the measurement results change when the dynamic response is changed, so it is necessary to compare under the same conditions.
The sound pressure level 0.3 seconds after the impact sound was generated was 71.8 dB for the Fast dynamic response (125 ms) and 44.8 dB for the 10 ms dynamic response, indicating that the shorter the dynamic response, the greater the attenuation of the sound pressure level.
Measuring the operating sound of "Newton's Cradle"
Figure 4 shows a portion of an Excel file (emm131-furiko.xls) used to calculate the A-weighted sound pressure level from the operating sound of a scientific toy called Newton's cradle (a pendulum consisting of five weights).
Columns A and B contain data obtained by reading 2.5 seconds of data from a WAVE file (sampling frequency 64 kHz) recorded using the sound recording function of the Oscope2 LA-3560 sound level meter, resampling it to a sampling frequency of 25.6 kHz, exporting it to a CSV file, and then importing it into Excel. Column A is the time, and column B is the instantaneous sound pressure [Pa].
The subsequent processing is the same as in the case of the sound of hitting a coffee can (empty can), but the sampling frequency is different, so the coefficients of the A-weighting filter are different.
Figures 5 and 6 show graphs of instantaneous sound pressure, instantaneous sound pressure (A-weighted), and A-weighted sound pressure level. The length of the horizontal axis of the graph corresponds to 2.5 seconds. Figure 5 shows the dynamic characteristic Fast (125 ms), and Figure 6 shows the dynamic characteristic 10 ms. The period of the pendulum is approximately 0.78 seconds, but since there are two collisions during one period, one from the right and one from the left, collision sounds are generated at intervals of approximately 0.39 seconds.
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Figure 5: Instantaneous sound pressure, instantaneous sound pressure (A-weighted), and A-weighted sound pressure level (dynamic characteristic Fast) of "Newton's Cradle".
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Figure 6: Instantaneous sound pressure, instantaneous sound pressure (A-weighted), and A-weighted sound pressure level (dynamic response 10 ms) of "Newton's cradle".
summary
The measurements described here can be easily performed using a sound level meter (with some exceptions) or real-time octave analysis software, but by performing the calculations described here, it is also possible to calculate them from instantaneous sound pressure data.
Please note that the calculation method using Excel is a simplified one. It does not conform to the sound level meter standards specified in JIS C 1509 or the Measurement Law. Furthermore, please understand that there is no guarantee that it meets the accuracy requirements specified in these standards.
The audio data (mp3 files) and Excel files used in this project can be downloaded from the link below.
Ono Sokki Technical Report: "What is a Sound Level Meter?"
(Excerpt from the email newsletter issued on August 23, 2012)
