Math Problem Statement
solve for the indicated value, and graph the situation showing the solution point. The formula for measuring sound intensity in decibels D is defined by the equation D=10log(I/I[0]) using the common (base 10) logarithm. where I is intensity of the sound in watts per square meter and I[0]=1-^-12 is the lowest level of sound that the average person can hear. How many decibels are emitted from a jet plane with a sound in tensity of 8.5*10^2 watts per square meter?
round answer to three decimal places.
Solution
The formula for measuring sound intensity in decibels (D) is given as:
where:
- is the intensity of the sound in watts per square meter,
- is the threshold of hearing, or the lowest intensity of sound the average person can hear.
We are given:
- watts per square meter.
We need to substitute these values into the formula to find .
Step-by-step Solution:
First, calculate the ratio inside the logarithm:
Now, take the logarithm (base 10) of :
So:
Now multiply by 10:
Final Answer:
The decibels emitted by the jet plane are approximately 149.290 dB.
Would you like me to generate a graph for this situation? Here are 5 related questions for further exploration:
- What is the intensity of sound at a decibel level of 100 dB?
- How does the sound intensity change as the decibel level increases by 10 dB?
- What is the decibel level for a sound with intensity watts per square meter?
- If the intensity of a sound increases tenfold, by how many decibels does the sound level increase?
- Can the decibel level ever be negative? If so, what does that represent?
Tip: When working with logarithms, recall that , which simplifies many calculations involving large numbers.
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Math Problem Analysis
Mathematical Concepts
Logarithms
Exponents
Sound Intensity
Formulas
D = 10 log(I/I0)
log(a * b) = log(a) + log(b)
Theorems
Properties of Logarithms
Sound Intensity to Decibel Conversion
Suitable Grade Level
Grades 11-12
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