Decibel Portfolio
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. Enter ENTER By the use of the
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. Enter ENTER By the use of the