1. What is the intensity of a sound at the pain level of 120 dB?
2. What is the intensity level of a sound whose intensity is 2.0 x 10^-6 W/m^2?
Use the equation you will find at
http://members.optusnet.com.au/scottsoftc/Chapter01/Chapter1f.htm
as well as your textbook, if you are using one.
0 dB corresponds to 10^-12 W/m^2 of sound intensity. Each 10 dB above that is a factor of 10.
1. To understand the intensity of a sound at a pain level of 120 dB, you need to know that decibels (dB) is a unit used to measure the relative loudness of a sound. The intensity of a sound is typically measured in watts per square meter (W/m^2).
To calculate the intensity level at 120 dB, you can use the formula:
IL = 10 * log10(I/I0)
Where IL is the intensity level in decibels, I is the intensity of the sound in watts per square meter, and I0 is the reference intensity, which is generally considered to be 1 x 10^-12 W/m^2.
So in this case, the intensity level can be calculated as:
IL = 10 * log10(I/1 x 10^-12)
Since the sound is at a pain level of 120 dB, the intensity level (IL) would be 120 dB. By rearranging the formula and solving for I, you can find the intensity of the sound:
120 = 10 * log10(I/1 x 10^-12)
Divide both sides of the equation by 10:
12 = log10(I/1 x 10^-12)
To get rid of the logarithm, convert the equation into exponential form:
10^12 = I/1 x 10^-12
Simplify the right side of the equation:
10^12 = I/10^-12
Multiply both sides of the equation by 10^-12:
10^12 * 10^-12 = I
10^0 = I
Therefore, the intensity of the sound at a pain level of 120 dB is 1 W/m^2.
2. To find the intensity level of a sound with an intensity of 2.0 x 10^-6 W/m^2, you can use the same formula mentioned above:
IL = 10 * log10(I/I0)
Where IL is the intensity level in decibels, I is the intensity of the sound in watts per square meter, and I0 is the reference intensity of 1 x 10^-12 W/m^2.
Substituting the given values:
IL = 10 * log10(2.0 x 10^-6 / 1 x 10^-12)
Simplifying the expression inside the logarithm:
IL = 10 * log10(2.0 x 10^6)
Taking the logarithm:
IL = 10 * 6
Multiplying:
IL = 60 dB
Therefore, the intensity level of a sound with an intensity of 2.0 x 10^-6 W/m^2 is 60 dB.