Question:

Solve exponential equations. Convert a logarithmic equation to exponential form and vice-versa. Read and solve applied problems including, but not limited to, compound interest and exponential growth and decay.

Consider the noise made by air plane taking off. One such takeoff of a jet generated a noise of 120 decibels. What is the intensity, I, of this sound?

Explanation

Sound energy is conveyed to our ears (or instruments) by means of a wave motion through some medium (gas, liquid, or solid). At any given point in the medium the energy content of the wave disturbance varies as the square of the amplitude of the wave motion. That is, if the amplitude of the oscillation is doubled, the energy of the wave motion is quadrupled. The common method in gauging this energy transport is to measure the rate at which energy is passing a certain point. This concept involves sound intensity. Consider an area that is normal to the direction of the sound waves. If the area is a unit, namely one square meter, the quantity of sound energy expressed in Joules that passes through the unit area in one second defines the sound intensity. The time rate of energy transfer is called "power". Thus, sound intensity is the power per square meter. The common unit of power is the Watt. Normally, sound intensity is measured as a relative ratio to some standard intensity, . The response of the human ear to sound waves closely follows a logarithmic function of the form R k logI , where R is the response to a sound that has an intensity of I, and k is a constant of proportionality. Thus, we define the relative sound intensity level (loudness) as: = 10 , which is measured in decibels (dB). I is the intensity of the sound expressed in watts per square meter (W/m2 ) and is a reference intensity defined to be 10-12 W/m2 . This value of is the threshold (minimum sound intensity) of hearing at 1 kHz for a young person under the best circumstances. For more information on sound and sound intensity, please visit https://www.physics.rutgers.edu/ugrad/301/PS08_Intensity_New.pdf