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Learning Goal: To learn the properties of logarithms and how to manipulate them when solving sound problems. The intensity of sound is the power of the sound waves divided by the area on which they are incident. Intensity is measured in watts per square meter, or W/m². The human ear can detect a remarkable range of sound intensities. The quietest sound that we can hear has an intensity of 10-12 W/m², and we begin to feel pain when the intensity reaches 1 W/m². Since the intensities that matter to people in everyday life cover a range of 12 orders of magnitude, intensities are usually converted to a logarithmic scale called the sound intensity level 3, which is measured in decibels (dB). For a given sound intensity I, B is found from the equation B = (10 dB) log(+). where Io = 1.0 x 10-1² W/m². The logarithm of z, written log(z), tells you the power to which you would raise 10 to get z. So, if y = log(z), then z = 10%. It is easy to take the logarithm of a number such as 10², because you can directly see what power 10 is raised to. That is, log(10²) = 2. ▾ Part A What is the value of log (1,000,000)? Express your answer as an integer. ► View Available Hint(s) log(1,000,000) = 6 Submit ✓ Correct Part B Previous Answers If a speaker gives a sound intensity of 10-6 W/m² at a certain point, what is the sound intensity level 3 at that point? Express your answer in decibels. ► View Available Hint(s) B= LIVD ΑΣΦ ? dB

Learning Goal: To learn the properties of logarithms and how to manipulate them when solving sound problems. The intensity of sound is the power of the sound waves divided by the area on which they are incident. Intensity is measured in watts per square meter, or W/m². The human ear can detect a remarkable range of sound intensities. The quietest sound that we can hear has an intensity of 10-12 W/m², and we begin to feel pain when the intensity reaches 1 W/m². Since the intensities that matter to people in everyday life cover a range of 12 orders of magnitude, intensities are usually converted to a logarithmic scale called the sound intensity level 3, which is measured in decibels (dB). For a given sound intensity I, B is found from the equation B = (10 dB) log(+). where Io = 1.0 x 10-1² W/m². The logarithm of z, written log(z), tells you the power to which you would raise 10 to get z. So, if y = log(z), then z = 10%. It is easy to take the logarithm of a number such as 10², because you can directly see what power 10 is raised to. That is, log(10²) = 2. ▾ Part A What is the value of log (1,000,000)? Express your answer as an integer. ► View Available Hint(s) log(1,000,000) = 6 Submit ✓ Correct Part B Previous Answers If a speaker gives a sound intensity of 10-6 W/m² at a certain point, what is the sound intensity level 3 at that point? Express your answer in decibels. ► View Available Hint(s) B= LIVD ΑΣΦ ? dB

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Learning Goal: To learn the properties of logarithms and how to manipulate them when solving sound problems. The intensity of sound is the power of the sound waves divided by the area on which they are incident. Intensity is measured in watts per square meter, or W/m². The human ear can detect a remarkable range of sound intensities. The quietest sound that we can hear has an intensity of 10-12 W/m², and we begin to feel pain when the intensity reaches 1 W/m². Since the intensities that matter to people in everyday life cover a range of 12 orders of magnitude, intensities are usually converted to a logarithmic scale called the sound intensity level 3, which is measured in decibels (dB). For a given sound intensity I, B is found from the equation B = (10 dB) log Io where Io = 1.0 × 10-¹² W/m². The logarithm of x, written log(x), tells you the power to which you would raise 10 to get x. So, if y = log(x), then x = 10%. It is easy to take the logarithm of a number such as 10², because you can directly see what power 10 is raised to. That is, log(10²) = 2. Part A What is the value of log (1,000,000)? Express your answer as an integer. ► View Available Hint(s) log (1,000,000) = 6 Submit Part B Correct B = Previous Answers If a speaker gives a sound intensity of 10-6 W/m² at a certain point, what is the sound intensity level 3 at that point? Express your answer in decibels. ► View Available Hint(s) [VD ΑΣΦ Submit ? Review I Constants dB
Transcribed Image Text:Learning Goal: To learn the properties of logarithms and how to manipulate them when solving sound problems. The intensity of sound is the power of the sound waves divided by the area on which they are incident. Intensity is measured in watts per square meter, or W/m². The human ear can detect a remarkable range of sound intensities. The quietest sound that we can hear has an intensity of 10-12 W/m², and we begin to feel pain when the intensity reaches 1 W/m². Since the intensities that matter to people in everyday life cover a range of 12 orders of magnitude, intensities are usually converted to a logarithmic scale called the sound intensity level 3, which is measured in decibels (dB). For a given sound intensity I, B is found from the equation B = (10 dB) log Io where Io = 1.0 × 10-¹² W/m². The logarithm of x, written log(x), tells you the power to which you would raise 10 to get x. So, if y = log(x), then x = 10%. It is easy to take the logarithm of a number such as 10², because you can directly see what power 10 is raised to. That is, log(10²) = 2. Part A What is the value of log (1,000,000)? Express your answer as an integer. ► View Available Hint(s) log (1,000,000) = 6 Submit Part B Correct B = Previous Answers If a speaker gives a sound intensity of 10-6 W/m² at a certain point, what is the sound intensity level 3 at that point? Express your answer in decibels. ► View Available Hint(s) [VD ΑΣΦ Submit ? Review I Constants dB
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