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
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18th Edition
ISBN:9781938168277
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Publisher:William Moebs, Samuel J. Ling, Jeff Sanny
Chapter16: Waves
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Problem 43P: (a) Seismographs measure the arrival times of earthquakes with a precision of 0.100 s. To get the...
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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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