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 explains how the loudness level of a sound is obtained 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?
10-2
Let A =
02-4
and b =
4
Denote the columns of A by a₁, a2, a3, and let W = Span {a1, a2, a̸3}.
-4 6
5
- 35
a. Is b in {a1, a2, a3}? How many vectors are in {a₁, a₂, a3}?
b. Is b in W? How many vectors are in W?
c. Show that a2 is in W. [Hint: Row operations are unnecessary.]
a. Is b in {a₁, a2, a3}? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your
choice.
○ A. No, b is not in {a₁, a2, 3} since it cannot be generated by a linear combination of a₁, a2, and a3.
B. No, b is not in (a1, a2, a3}
since b is not equal to a₁, a2, or a3.
C. Yes, b is in (a1, a2, a3} since b = a
(Type a whole number.)
D. Yes, b is in (a1, a2, 3} since, although b is not equal to a₁, a2, or a3, it can be expressed as a linear
combination of them. In particular, b =
+
+
☐ az.
(Simplify your answers.)
14
14
4. The graph shows the printing rate of Printer A. Printer B can
print at a rate of 25 pages per minute. How does the printing
rate for Printer B compare to the printing rate for Printer A?
The printing rate for Printer B is
than the rate
for Printer A because the rate of 25 pages per minute
is
than the rate of
for Printer A.
pages per minute
RIJOUT
40
fy
Printer Rat
Number of Pages
8N WA
10
30
20
Printer A
0
0
246
Time (min)
X
OR
16 f(x) =
Ef 16
χ
по
x²-2 410 | y = (x+2) + 4
Y-INT: y = 0
X-INT: X=0
VA: x=2
OA: y=x+2
0
X-INT: X=-2
X-INT: y = 2
VA
0
2
whole.
2-2
4
y - (x+2) = 27-270
+
xxx> 2
क्
above OA
(x+2) OA
x-2/x²+0x+0
2
x-2x
2x+O
2x-4
4
X<-1000 4/4/2<0 below Of
y
VA
X=2
X-2
OA
y=x+2
-2
2
(0,0)
2
χ
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