Decibel Portfolio Essay -- essays research papers

The intensity I of a sound wave is measured in watts per metre squared ( ). The lowest intensity that the average human ear can detect, i.e. the threshold of hearing, is denoted by , where . The loudness of sound, i.e. its intensity level , is measured in decibels (dB), where . From this function a specific relationship between and can be drawn that holds true for any increase in intensity. By knowing the value of beta ( ), the value of can be found via manipulation of the logarithmic function, and by knowing the value of beta can by found by just taking the log of and multiplying it by ten. The intensity level of ordinary conversation is 65 dB. In order to find the intensity of normal conversation on must set beta to 65 dB and to . Afterwards, via using the division property of equality one joins like terms. Once the logarithm is alone, one can apply the properties of logarithms and separate the logarithm into two logarithms. The quotient rule for logarithms is applied to this equation, , where and . By the definition of the logarithmic function, if and only if , one knows that in order to cancel out the logarithm one must exponentiate the log to ten. When one does this one must also keep in mind that equality must be kept on both sides of the equation, so the -5.5 becomes the exponent of ten. After doing this, one knows that . dB . If one wanted to find the intensity of the sound inside and automobile travelling at that has an intensity level of 75 dB one would follow the same procedure mentioned previously to find intensity. In addition to this method one can use a graphing calculator in order to make the finding of I simpler. By following the procedure one can use a Ti-82 graphing calculator to find the intensity I of a sound by knowing the intensity level b. The function used is just all the steps followed above summarized into one function.   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Enter   Ã‚  Ã‚  Ã‚  Ã‚  ENTER By the use of the calculator, one finds the correct response in a quicker fashion than by working the problem out. However, in order to prove that the answer provided by the calculator is correct one should always work out the problem by hand. dB  Ã‚  Ã‚  Ã‚  Ã‚   Source of Sound  Ã‚  Ã‚  Ã‚  Ã‚  Intensity Level (dB)  ... ...even though the has changed, if the intensity level increases by ten units, then the intensity increases ten times. When me and my dog cross a busy street the noise does not seem equally loud to both of us. This because the dog has a higher threshold of hearing than me. This is explained best by the fact that the graph for the intensity level in terms of intensity for dogs is translated ten units up from the one for humans. The vertical translation signifies that for any given intensity, the intensity level is ten dB more for dogs than for humans. Knowing the relationship between intensity I and the intensity level b is very important to understanding how all beings hear. By understand the relationship, we know that the threshold of something’s hearing is what affects loudness with which it hears the sound. Furthermore, by understanding the relationship we know that the curve for the relationship will always have the same shape, but the only difference will be that for different thresholds, it will be translated along the Y-axis. Throughout this project, it was researched how to use properties of logarithms in order to assist one in finding intensity by knowing intensity level,