A. When we are designing the sound levels to ensure a clear reception by a human ear, we often express the sound intensity in a unit called dB. The intensity level in dB of a sound wave can be found by converting the sound intensity produced by the speakers, I, expressed in Watts/m2, using the formula: B(dB) = 10log10(G) Where: B is the sound intensity level in dB. I is the sound wave intensity in W/m2. lo is a constant representing the intensity threshold of hearing, which is the lowest intensity a human can hear with his/her ears. A sound source, or a speaker, produces a wave with intensity I, which varies with respect to time as given below: I = 3 + 2 cos(4t-n) W/m2. Knowing that Io = 1 x 10-12 W/m²: 1. Find a formula for the rate of change of B with respect to time. [Hint: use the chain rule] 2. Find the value of the rate of change of ß with respect to time at t = 1 sec. %3D

Introductory Circuit Analysis (13th Edition)
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A. When we are designing the sound levels to ensure a clear reception by a human ear, we often express
the sound intensity in a unit called dB. The intensity level in dB of a sound wave can be found by
converting the sound intensity produced by the speakers, I, expressed in Watts/m2, using the formula:
B(dB) = 10log10(G)
Where:
B is the sound intensity level in dB. I is the sound wave intensity in W/m2. lo is a constant representing the
intensity threshold of hearing, which is the lowest intensity a human can hear with his/her ears.
A sound source, or a speaker, produces a wave with intensity I, which varies with respect to time as given
below:
I = 3 + 2 cos(4t-n) W/m2.
Knowing that Io = 1 x 10-12 W/m²:
1. Find a formula for the rate of change of B with respect to time. [Hint: use the chain rule]
2. Find the value of the rate of change of ß with respect to time at t = 1 sec.
%3D
Transcribed Image Text:A. When we are designing the sound levels to ensure a clear reception by a human ear, we often express the sound intensity in a unit called dB. The intensity level in dB of a sound wave can be found by converting the sound intensity produced by the speakers, I, expressed in Watts/m2, using the formula: B(dB) = 10log10(G) Where: B is the sound intensity level in dB. I is the sound wave intensity in W/m2. lo is a constant representing the intensity threshold of hearing, which is the lowest intensity a human can hear with his/her ears. A sound source, or a speaker, produces a wave with intensity I, which varies with respect to time as given below: I = 3 + 2 cos(4t-n) W/m2. Knowing that Io = 1 x 10-12 W/m²: 1. Find a formula for the rate of change of B with respect to time. [Hint: use the chain rule] 2. Find the value of the rate of change of ß with respect to time at t = 1 sec. %3D
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