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Try It 10.51: Calculating the Decibel Level of a Dishwasher
To determine the decibel level of a quiet dishwasher with an intensity of watts per square inch, use the decibel level formula D = 10 \log\left(\frac{I}{10^{-12}} ight). Substituting the given intensity, , into the formula yields D = 10 \log\left(\frac{10^{-7}}{10^{-12}} ight). Simplifying the expression inside the logarithm gives . Since , the decibel level evaluates to , which equals dB.
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Intermediate Algebra @ OpenStax
Ch.10 Exponential and Logarithmic Functions - Intermediate Algebra @ OpenStax
Algebra
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Example 10.26: Calculating the Decibel Level of Earphones
Try It 10.51: Calculating the Decibel Level of a Dishwasher
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Input Validation for Common Logarithmic Data
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Learn After
A property manager is evaluating the noise specifications for appliances in a new office suite. Using the decibel level formula , what is the decibel level () for a dishwasher model that has a sound intensity of watts per square inch?
A facility manager is documenting the noise levels of appliances for a new building project. A quiet dishwasher model is listed with a sound intensity of watts per square inch. Arrange the mathematical steps in the correct order to determine its decibel level using the formula .
A facility manager is documenting the noise specifications for kitchen appliances. Match each numerical value from the decibel calculation formula with its correct role or meaning when calculating the noise level of a quiet dishwasher.
A facility manager is documenting the noise specifications for a quiet dishwasher model. According to the decibel level formula , a dishwasher with a sound intensity of watts per square inch has a calculated noise level of 50 decibels.
An occupational health and safety officer is verifying the noise specifications for a new breakroom dishwasher. The appliance has a rated sound intensity of watts per square inch. When substituting this into the decibel formula , the expression simplifies to , which evaluates to a final noise rating of ____ decibels.