Use this technique to find a formula for the intensity I of a sound, in terms of the sound level β and the reference intensity I0. There will be a quantity (10 dB) involved in your calculations. When you enter your answer, leave off the unit dB. Express your answer in terms of β and I0.

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  • Use this technique to find a formula for the intensity I of a sound, in terms of the sound level β and the reference intensity I0. There will be a quantity (10 dB) involved in your calculations. When you enter your answer, leave off the unit dB.
    Express your answer in terms of β and I0.
     
     
     
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 In = 1.0 × 10-¹2 W/m².
Transcribed Image Text: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 In = 1.0 × 10-¹2 W/m².
In the introduction, the logarithm of a was defined as the power to which you would raise 10 to get . This can be written as
10log(z) = I.
You can use this formula to solve equations like log(x) = 4.3. Since log(x) is equal to 4.3, it must also be true that
10log(z) = 104.3
This formula now allows you to replace the left side of the equation with z, giving a =
104.3
Transcribed Image Text:In the introduction, the logarithm of a was defined as the power to which you would raise 10 to get . This can be written as 10log(z) = I. You can use this formula to solve equations like log(x) = 4.3. Since log(x) is equal to 4.3, it must also be true that 10log(z) = 104.3 This formula now allows you to replace the left side of the equation with z, giving a = 104.3
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