DiegoA_Acoustics_Lab7

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Submitted By: Diego Arpino Section: ME343-101 Date Performed: 12/05/2023 Date Submitted: 12/12/2023 Sign : Diego A. Group Name: 3 Group Members: Diego, Beatriz, Jessica, Mahmoud, Carlos, Richard, David, Paul NEW JERSEY INSTITUTE OF TECHNOLOGY ME-343 Mechanical Systems laboratory-I, Fall 2023 MECHANICAL AND INDUSTRIAL ENGINEERING DEPARTMENT Acoustics Instructor : Dr. Trivikrama Reddy By signing above, you confirm that only you have contributed to this submission. Any suspicion of copying or plagiarism in this work will result in an investigation of Academic Misconduct and may result in a “0” on the work, an “F” in the course, or possibly more severe penalties as well as a Disciplinary Notice on your academic record under the Academic Honor Code, which can be found online at: http://www5.njit.edu/doss/policies/honorcode/article3.php

Abstract This experiment investigates sound intensity variations with respect to the distance from a sound source in a controlled environment. Utilizing precision sound pressure level monitors, measurements were conducted at two distances from the source. The research aims to show the relationship between distance and sound intensity, examining the adherence to principles governing sound wave dissipation, notably the inverse square law. Through systematic data collection and analysis, the experiment offers insights into the behavior of sound waves in unobstructed spaces, reinforcing theoretical concepts and providing practical understanding of sound transmission.

Acoustics Table of Contents Introduction ------------------------------------------------------------------------------------------ 1 Definitions and Nomenclature -------------------------------------------------------------------- 1 Theoretical Principles ------------------------------------------------------------------------------ 2 Experimental System ------------------------------------------------------------------------------- 5 Results and Discussion ----------------------------------------------------------------------------- 8 Conclusion ------------------------------------------------------------------------------------------- 8 References ------------------------------------------------------------------------------------------- 9 Images Image 1: Transverse Waveform ------------------------------------------------------------------- 2 Image 2: Longitudinal Waveform ---------------------------------------------------------------- 2 Image 3: dual speaker set-up, showing the first monitor 4.5 feet away --------------------- 5 Image 4: the monitor 4.5 feet from the source --------------------------------------------------- 6 Image 5: the monitor 4.5 feet from the first monitor, and 9 feet from the source ---------- 6 Image 6: control system of the set-up ------------------------------------------------------------- 7 Table of Figures Figure 1: Schematic of the experimental system ----------------------------------------------- 5 Figure 2: SPL Change with speaker output ----------------------------------------------------- 8

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1 Intro This experiment investigates sound intensity variation by measuring levels at different distances from a source. Using two acoustic sensors, sound intensity was measured at two points from the source: 4.5 feet and 9 feet away. The main objective of this experiment is to understand the inversely square relationship between the intensity change of the sound with distance, shedding light on the principles of sound propagation in an open space. Definitions and Nomenclature Sound - an oscillation of pressure transmitted through a medium, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard. Decibel (dB) – a unit used to measure the intensity or power of a sound wave Sound Pressure Level (SPL) – the logarithmic measurement of the magnitude of a sound wave's pressure variations Medium – the material or substance through which a sound wave travels, composed of solid, liquid, or gas Sound Velocity – The speed that sound waves propagate through a medium Wave – a disturbance that travels through a medium, transferring energy Transverse Wave – a waveform in which oscillations are perpendicular to the direction of propagation Longitudinal Wave – a waveform in which oscillations are parallel to the direction of propagation

2 Theoretical Principles There are two different types of waveforms, transverse and longitudinal, as shown below: Image 1: Transverse Waveform Image 2: Longitudinal Waveform These were defined earlier. However, because sound propagates as a longitudinal wave, that waveform will be the focus of discussion, and the transverse form will be disregarded. We are familiar that the Sound Pressure level (SPL), of a singular wave is a measure of the intensity of the sound wave, and it is given by the following equation: ࠵?࠵?࠵? = 20log ( ࠵? !"# ࠵? !$% )࠵?࠵? Where p rms represents the effective sound pressure, and p ref represents the reference value, which is usually 20 × 10 &’ ( ) ! , which is regarded as the faintest sound pressure that the human ear is able to detect. Because this experiment utilizes two sound sources, we must become familiar with the calculations needed to calculate the SPL of multiple waves of both identical and different frequency. We derive these on the following page:

3 When these equations are integrated, we are left with two cases: one in which the frequencies and phases are the same, and one where they are different.

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4 Because the measurement is of a logarithmic scale, we can also deduce that the audible intensity of a sound wave is inversely proportional to the square of the distance from the sound source. Assuming a setup that consists of a source and two instruments that detect the intensity that are of the following parameters, we obtain the following: This shows that ideally, with a double in distance from the source, the reading of the second pressure monitor that is 9 feet from the source should theoretically read about 6 dB lower than the first monitor. It is worth noting that the setup used in the experiment consisted of the same distances, however there were two speakers acting as the sound sources, and that other noise factors could affect these readings, such as possible noise from outside the acoustic chamber, interference from the ventilation system, mechanical noise from the speakers, and even electrical hum from the electrical system

5 Experimental System The experimental system consisted of two speakers, and two sound level monitors inside of an acoustically isolated chamber. One of the two monitors was placed 4.5 feet from the source speakers, and the other was placed another 4.5 feet behind th e first monitor, which was also 9 feet away from the source speakers. A schematic is shown below: Figure 1: Schematic of the experimental system Images of the setup are also shown Image 3: dual speaker set-up, showing the first monitor 4.5 feet away

6 Image 4: the monitor 4.5 feet from the source Image 5: the monitor 4.5 feet from the first monitor, and 9 feet from the source

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7 Image 6: control system of the set-up The data recording portion of the experiment consisted of the following steps in order: 1. The acoustic was closed and the speakers were off 2. Speaker 1 was turned on 3. Speaker 2 was turned on, meaning that both speakers were now on 4. Speaker 1 was turned off 5. Speaker 2 was turned off The data was recorded over the course of about 140 seconds, with intervals of 0.1 seconds and a decibel reading from each SPL monitor for each interval. The results of the experiment are shown on the following page.

8 Results and Discussion Using the data points, a graph of the SPL readings with time is shown below: Figure 2: SPL Change with speaker output The steps of the events of the procedure are quite evident just by observing the graph. At about 17 seconds, we can see a noticeable jump in the SPL when Speaker 1 was turned on. We also notice two spikes in the data at about 23 seconds and 32 seconds, and this is due to a noise error interference. We see the SPL jump again at 40 seconds, and this is due to Speaker 2 being turned on. We once again notice a spike in the data due to unwanted noise. At 60 seconds, Speaker 1 is turned off, and the SPL readings drop back down, and then we see the SPL gradually decrease when Speaker 2 is finally turned off. The reason for a gradual decrease instead of an instant change is because the mechanical energy of the speakers and vibrations in the system persist for some time. Conclusion We can see from the results that the increases in intensity correspond quite nicely to the changes in the speaker settings, and when the speakers are on, we can observe a difference in the SPL levels of around 6 dB, which matches the earlier calculations. This concludes a successful experiment. 0 10 20 30 40 50 60 70 80 90 100 0 20 40 60 80 100 120 140 160 SPL (dB) Time (s) SPL Change with Speaker Output Monitor 1 (4.5ft) Monitor 2 (9ft)

9 References Mechanical Laboratory 1, Module 8, Acoustics, Dr. Trivikrama Pala Experimental Methods for Engineers, 8 th Edition, Chapter 11, J.P. Holman

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