Deriving Equations for School Administration

One monday, I represented the student body in lieu of Charles, the COA president. The agenda was about MVP rules and guidelines. An issue was raised about the noised levels. As the science major and head of the science guild, I thought that the rule of benchmarking permits with a karaoke device lacks a quantitative aspect given that we are in a university setting and exercises a high degree of scholarship. So I was tasked to create a recommended sound levels for student activities.

The decibel scale for sound intensity has a standard comparison to everyday sound environments[1]. 70 dB is the intensity of conversational speech. With this I played around certain properties. The first information that was needed was to determine the relationship of sound intensity against distance traveled. When not using the decibel scale sound intensity is expressed as

[tex] I = \frac{P}{A} [/tex]

where P is power in watts and A is in meters squared. Assuming that sound travels a distance R, the equation can be reexpressed as

[tex] I = \frac{P}{C r^2} [/tex]

where C is some constant. Taking this into consideration in the new decibel measurements the new level will be

[tex] \beta = 10 \left{ \log \frac{P}{C} – \log I_0 – 2 \log R \right}[/tex]

This means that if there is an org activity at the MVP basement or roofdeck having an noise level of 85 decibels, the nearest offices (approximately 100 meters away) in Kostka, Faura and dela Costa will perceive a sound intensity attenuated by 20 decibels (20log100). This sound level of 65 decibel is well below conversational speech.

[1] Decibel Sound Pressure Level Example Chart.
[2] Maron, J and W Hornyak. 1982. Physics For Science and Engineering. Saunders College Publishing

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3 Responses to “Deriving Equations for School Administration”

  1. 2 Dean Michael Berris 2006 9月 6 1:13 am

    Nice equation(s) there. However, you have only shown the mathematical property when you assume that the sound intensity does not degrade over a distance as affected by environmental factors like humidity, the type of air in the area, and that you assumed that the sound travels in a radial (non-spherical) 2 dimensions and that the source is not near a wall/floor. The effect of how far a sound is from the sounding board or the nearest thing that allows the vibration to actually amplify (like the floor, or a wall, etc.) will affect the intensity and _quality_ of the “noise” or sound as the environmental factors (as you have not considered) will affect the sound gathered from the other end.

    The frequency of the sound also affects the dampening effect that the air around the source plays. You’ll need at least a few more factors to accurately find out how much “noise” actually reaches a certain point in space given reallistic environmental factors.

    However, the equations seem enough to convince someone that the sound that reaches the other end of the hall is not noisy enough. 🙂

  2. 3 Allan Espinosa 2006 9月 6 1:32 am

    Thanks for the feedback Dean :D. I forgot to include in the original post that one of my assumptions was that the sound travels along free space. I have thought of protocols in which how the school can measure the sound source. The intensity of the point source can be measured using special equipment on exits of a building like windows and doors. Although this is a crude method, it can be assumed that the sound from these parts can be representatives of a point source for practical purposes for the school.


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Allan M. Espinosa

Currently based in Tokyo, Japan
DevOps Engineer at Rakuten, Inc.