Sounds are produced when vibrating objects create pressure waves in some medium such as air. When these variations in pressure reach the human eardrum, it causes the eardrum to vibrate in a similar manner and the ear detects sound. The intensity of sound is measured as power per unit area. The threshold for hearing (minimum sound detectable by a young, healthy ear) is defined to be I 0 = 10 − 12 W / m 2 (watts per square meter). The sound level L , or “loudnessâ€� of sound, is measured in decibels (dB) as L = 10 log I I 0 , where I is the intensity of the given sound. Use this formula for Exercises 95-96. a. Find the sound level of a motorcycle if its intensity is 10 10 times I 0 . b. Find the sound level of a vacuum cleaner if its intensity is 10 7 times I 0 . c. How many times more intense is the sound of a motorcycle than a vacuum cleaner?
Sounds are produced when vibrating objects create pressure waves in some medium such as air. When these variations in pressure reach the human eardrum, it causes the eardrum to vibrate in a similar manner and the ear detects sound. The intensity of sound is measured as power per unit area. The threshold for hearing (minimum sound detectable by a young, healthy ear) is defined to be I 0 = 10 − 12 W / m 2 (watts per square meter). The sound level L , or “loudnessâ€� of sound, is measured in decibels (dB) as L = 10 log I I 0 , where I is the intensity of the given sound. Use this formula for Exercises 95-96. a. Find the sound level of a motorcycle if its intensity is 10 10 times I 0 . b. Find the sound level of a vacuum cleaner if its intensity is 10 7 times I 0 . c. How many times more intense is the sound of a motorcycle than a vacuum cleaner?
Sounds are produced when vibrating objects create pressure waves in some medium such as air. When these variations in pressure reach the human eardrum, it causes the eardrum to vibrate in a similar manner and the ear detects sound. The intensity of sound is measured as power per unit area. The threshold for hearing (minimum sound detectable by a young, healthy ear) is defined to be
I
0
=
10
−
12
W
/
m
2
(watts per square meter). The sound level
L
,
or “loudness� of sound, is measured in decibels (dB) as
L
=
10
log
I
I
0
,
where
I
is the intensity of the given sound. Use this formula for Exercises 95-96.
a. Find the sound level of a motorcycle if its intensity is
10
10
times
I
0
.
b. Find the sound level of a vacuum cleaner if its intensity is
10
7
times
I
0
.
c. How many times more intense is the sound of a motorcycle than a vacuum cleaner?
1. Show that the vector field
F(x, y, z)
=
(2x sin ye³)ix² cos yj + (3xe³ +5)k
satisfies the necessary conditions for a conservative vector field, and find a potential function for
F.
1. Newton's Law of Gravitation (an example of an inverse square law) states that the magnitude
of the gravitational force between two objects with masses m and M is
|F|
mMG
|r|2
where r is the distance between the objects, and G is the gravitational constant. Assume that the
object with mass M is located at the origin in R³. Then, the gravitational force field acting on
the object at the point r = (x, y, z) is given by
F(x, y, z) =
mMG
r3
r.
mMG
mMG
Show that the scalar vector field f(x, y, z) =
=
is a potential function for
r
√√x² + y² .
Fi.e. show that F = Vf.
Remark: f is the negative of the physical potential energy, because F = -V(-ƒ).
2. Suppose f(x) = 3x² - 5x. Show all your work for the problems below.
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