The loudness level of a sound can be expressed by comparing the sound's intensity to the intensity of a sound barely audible to the human ear. The formula D = 10 ( log I − log I 0 ) describes the loudness level of a sound, D , in decibels, where I is the intensity of the sound, in watts per meter 2 , and I 0 is the intensity of a sound barely audible to the human ear. a. Express the formula so that the expression in parentheses is written as a single logarithm. b. Use the form of the formula from part (a) to answer this question; If a sound has an intensity 100 times the intensity of a softer sound, how much larger on the decibel scale is the loudness level of the more intense sound?
The loudness level of a sound can be expressed by comparing the sound's intensity to the intensity of a sound barely audible to the human ear. The formula D = 10 ( log I − log I 0 ) describes the loudness level of a sound, D , in decibels, where I is the intensity of the sound, in watts per meter 2 , and I 0 is the intensity of a sound barely audible to the human ear. a. Express the formula so that the expression in parentheses is written as a single logarithm. b. Use the form of the formula from part (a) to answer this question; If a sound has an intensity 100 times the intensity of a softer sound, how much larger on the decibel scale is the loudness level of the more intense sound?
Solution Summary: The author calculates the loudness level of a sound by formula underset_D=mathrmlog(m
The loudness level of a sound can be expressed by comparing the sound's intensity to the intensity of a sound barely audible to the human ear. The formula
D
=
10
(
log
I
−
log
I
0
)
describes the loudness level of a sound, D, in decibels, where I is the intensity of the sound, in watts per meter2, and I0 is the intensity of a sound barely audible to the human ear.
a. Express the formula so that the expression in parentheses is written as a single logarithm.
b. Use the form of the formula from part (a) to answer this question; If a sound has an intensity 100 times the intensity of a softer sound, how much larger on the decibel scale is the loudness level of the more intense sound?
1. A bicyclist is riding their bike along the Chicago Lakefront Trail. The velocity (in
feet per second) of the bicyclist is recorded below. Use (a) Simpson's Rule, and (b)
the Trapezoidal Rule to estimate the total distance the bicyclist traveled during the
8-second period.
t
0 2
4 6 8
V
10 15
12 10 16
2. Find the midpoint rule approximation for
(a) n = 4
+5
x²dx using n subintervals.
1° 2
(b) n = 8
36
32
28
36
32
28
24
24
20
20
16
16
12
8-
4
1
2
3
4
5
6
12
8
4
1
2
3
4
5
6
=
5 37
A 4 8 0.5
06
9
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
Chapter 3 Solutions
MyLab Math with Pearson eText -- Standalone Access Card -- for Precalculus (6th Edition)
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