Mid -Term 2

Question 1

In order to study something about the deci____, we must first review some information about the logarithm.

Answer 1

bel

Question 2

Logarithms are simply exponents, and you know what an exponent is: In the expression 10² = 100, 2 is an _______.

Answer 2

exponent

Question 3

We have already said that a logarithm is an _______.

Answer 3

exponent

Question 4

Therefore, the number 2 in the expression 10² is both an exponent and a _______.

Answer 4

logarithm

Question 5

In the expression 10² , the number 2 tells us to take the number 10 two times like this: 10 x 10 = ____, which is the same as 10² = 100.

Answer 5

100

Question 6

Thus 10³ means the number 10 taken _____ times or

10 x 10 x 10= 1000.

Answer 6

3

Question 7

In the expression 10³ , the number 10 is called the base, and the number _____ is the exponent or logarithm.

Answer 7

3

Question 8

In the expression 4³ and 10³, the exponent is 3 in each case, but the base is _______ and 10 respectively.

Answer 8

4

Question 9

In the expression 10⁵ we mean take 10 ________ times as in 10 x 10 x 10 x 10 x 10 = 100,000.

Answer 9

5

Question 10

Thus, 10³= _________.

Answer 10

1000

Question 11

While 10⁵ = ____________.

Answer 11

10000

Question 12

The logarithm in the expression 10⁵ is the number _______, while the base is the number _________.

Answer 12

5, 10

Question 13

In dealing with _______bels, the logarithm (or log) to which we refer, will always have a base of 10.

Answer 13

deci

Question 14

Thus, we can answer, 10² = 100 is the same as the log of 100 is___.

Answer 14

2

Question 15

10³ = 1,000 or the _________ of 1,000 is 3.

Answer 15

log

Question 16

The log of 1,000 is _____.

Answer 16

3

Question 17

You may have noticed that the exponent tells you how many zeros appear after the number 1. Thus 10² is the number one followed by ______ zeros.

Answer 17

2

Question 18

10³ is the number one followed by 3 _______.

Answer 18

zeros

Question 19

Thus it is orderly the 10¹ is the number one with __________ zero, or the number 10.

Answer 19

one

Question 20

It remains orderly when we say, therefore, that 10⁰ = 1, because we are saying 10⁰ equals the number one with _______ zeros following.

Answer 20

no

Question 21

10⁰ = ______.

Answer 21

1

Question 22

The logarithm of 1 is _______.

Answer 22

0

Question 23

Note again the ________________ of 1 is zero.

Answer 23

logarithm

Question 24

The log of 1,000 = _________.

Answer 24

3

Question 25

The log of 100 = _________.

Answer 25

2

Question 26

The log of 1 = ________.

Answer 26

zero

Question 27

The log of _________ = zero.

Answer 27

1

Question 28

We should review a bit about ratios. If we divide a number by itself, as in 198/198, we get a ratio of 1. Thus if we divide 3,456 by 3,456 we still get ______.

Answer 28

1

Question 29

If we divide .002 by .002 we still get _________.

Answer 29

1

Question 30

If we divide .002 by _________ we still get 1

Answer 30

.002

Question 31

Regardless of which numbers we choose, if you divide a number by itself, you will always get _______.

Answer 31

1

Question 32

If you divide .002 by .0002 you get 10. Thus .002/.0002 = _____.

Answer 32

10

Question 33

If you divide .02 by .0002 you get 100. Thus, .02/.0002 = ______.

Answer 33

100

Question 34

But if you divide .0002 by _________ you get 1.

Answer 34

.0002

Question 35

Now study the equation:* No. of decibels = 20 x log P₁/P₂ P₁ = the output of the speaker or earphone in units of pressure. P₂ = our arbitrarily chosen reference level in units of pressure.

Answer 35

* If you expected to read that 10 x log P₁/P₂ read the following footnote: Footnote: You will note that this equation is a pressure equation, already derived from a power formula. For reasons of conservation of space, the derivation of pressure from power formula has been deleted.

Question 36

P₁ = the output of the speaker or earphones in units of _________________.

Answer 36

pressure

Question 37

P₂ = Our __________________ chosen reference level in units of pressure.

Answer 37

arbitrarily

Question 38

P₂ = Our arbitrarily chosen __________________ level in units of pressure.

Answer 38

reference

Question 39

To solve the equation we first find the numerical value of the ratio expressed by P₁ over _________.

Answer 39

P2

Question 40

Then we find the loga-__________ of that value.

Answer 40

rithm

Question 41

Then we multiply the resulting expression by _________.

Answer 41

20

Question 42

Note that first we must find the numerical value of the ____________ expressed by P₁ over P₂ .

Answer 42

ratio

Question 43

Once we have found the numerical value of the ratio, we must then find the ________________ of the numerical value.

Answer 43

logarithm

Question 44

Once we have the logarithm of the ratio we _______________ it by 20.

Answer 44

multiply

Question 45

If the ratio is one, that is, when P₁ = _______, we know that the logarithm of one is zero, then the entire equation will yield a value of ______________.

Answer 45

P2, zero

Question 46

Thus, zero dB does not mean silence, or absence of sound; it simply means that the output of our speaker or phone is exactly ______________ to the arbitrary reference level we have chosen.

Answer 46

equal

Question 47

Should we change the ratio of _______ over P₂ to a ratio of 100, then since the log of 100 is _____, we have 20 x 2 = _____ dB.

Answer 47

P1, 2, 40

Question 48

Suppose our pressure ratio were changed to 1,000. Then the _________________ of 1,000 is 3 and thus we have _______ x 3 = 60.

Answer 48

logarithm, 20

Question 49

Now suppose we generate 10,000 times the pressure of our arbitrary reference level. Then the log of 10,000 is ______ and the resultant decibel value is _______.

Answer 49

4, 80

Question 50

A decibel therefore has no true dimension of its own. This is because the value P₂ in our equation is purely _____________, that is, it can be any value you choose.

Answer 50

arbitrary

Question 51

For the sake of convenience, as well as other reasons pertaining to an electrical power reference, acoustical scientists often choose 0.0002 dyne/cm2 as a reference point from which to make sound pressure level measurements. Sound _______________ level measurements therefore are often based on 0.0002 ___________/ cm² .

Answer 51

pressure, dyne

Question 52

Sound Pressure Level is often abbreviated S. P. ____.

Answer 52

L.

Question 53

Thus, if you see in a text that a sound was given at 65dB SPL it means that the reference level was probably 0.000___ Dyne/cm² . Note: You don't have to do math for this, just remember the equation.

Answer 53

2

Question 54

A sound given at 40dB ___ PL has as its reference point, 0.0002 dyne per square centimeter.

Answer 54

S

Question 55

A sound given at 55dB SPL has as its reference point ________ dyne/cm² .

Answer 55

0.0002

Question 56

Thus, the abbreviation ________ means specifically sound pressure level, and usually implies that the reference point of 0 decibels is ______________________.

Answer 56

SPL, 0.0002 dynes/cm²

Question 57

Now, let's review. | Decibels are logarithmic numbers, so we must understand the lo-________________ to understand the decibel.

Answer 57

garithm

Question 58

The log of 1000 is ______.

Answer 58

3

Question 59

The log of 100 is ______.

Answer 59

2

Question 60

The log of 10 is ______.

Answer 60

1

Question 61

The log of 1 is ______.

Answer 61

0

Question 62

The log of _________ is 3.

Answer 62

1,000

Question 63

The log of _________ is 2.

Answer 63

100

Question 64

The log of _________ is 1.

Answer 64

10

Question 65

The log of _________ is 0.

Answer 65

1

Question 66

When we use a pressure reference the equation for determining the number of decibels reads: No. dB = 20 x ________ P₁/P₂.

Answer 66

log

Question 67

When we use a pressure reference the equation for determining the number of decibels reads: No. dB = 20 x ________ P₁/P₂.

Answer 67

log

Question 68

No. dB = _______ x log P₁/P₂ where P₂ is pressure reference.

Answer 68

20

Question 69

Number of dB = 20 x log __________.

Answer 69

P1/P2

Question 70

When P₁ over P₂ is equal to 1, we have a log value of ___________.

Answer 70

zero

Question 71

With a value of zero in the equation, the number of dB is also ________.

Answer 71

zero

Question 72

Therefore, 0 dB is obtained when P₁ equals P₂, or when the ratio is ___________.

Answer 72

1

Question 73

Thus zero dB does not mean silence, or no sound; it means P₁ = ________.

Answer 73

P2

Question 74

In the measurement of sound pressure level, P₂ is often arbitrarily set at 0.0002 dyne/______.

Answer 74

cm²

Question 75

A common arbitrary reference point from which to make measurements of sound pressure is 0.000_________________.

Answer 75

2 dynes/cm²

Question 76

The common reference point from which we make measurements of sound pressure is ______________________.

Answer 76

0.0002 dynes/cm²