Flashcards in Mid -Term 2 Deck (76):

1

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

### bel

2

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

### exponent

3

## We have already said that a logarithm is an _______.

### exponent

4

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

### logarithm

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.

### 100

6

##
Thus 10³ means the number 10 taken _____ times or

10 x 10 x 10= 1000.

### 3

7

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

### 3

8

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

### 4

9

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

### 5

10

## Thus, 10³= _________.

### 1000

11

## While 10⁵ = ____________.

### 10000

12

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

### 5, 10

13

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

### deci

14

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

### 2

15

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

### log

16

## The log of 1,000 is _____.

### 3

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.

### 2

18

## 10³ is the number one followed by 3 _______.

### zeros

19

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

### one

20

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

### no

21

## 10⁰ = ______.

### 1

22

## The logarithm of 1 is _______.

### 0

23

## Note again the ________________ of 1 is zero.

### logarithm

24

## The log of 1,000 = _________.

### 3

25

## The log of 100 = _________.

### 2

26

## The log of 1 = ________.

### zero

27

## The log of _________ = zero.

### 1

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 ______.

### 1

29

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

### 1

30

## If we divide .002 by _________ we still get 1

### .002

31

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

### 1

32

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

### 10

33

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

### 100

34

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

### .0002

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.

###
* 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.

36

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

### pressure

37

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

### arbitrarily

38

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

### reference

39

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

### P2

40

## Then we find the loga-__________ of that value.

### rithm

41

## Then we multiply the resulting expression by _________.

### 20

42

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

### ratio

43

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

### logarithm

44

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

### multiply

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 ______________.

### P2, zero

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.

### equal

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.

### P1, 2, 40

48

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

### logarithm, 20

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 _______.

### 4, 80

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.

### arbitrary

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 .

### pressure, dyne

52

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

### L.

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.

### 2

54

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

### S

55

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

### 0.0002

56

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

### SPL, 0.0002 dynes/cm²

57

##
Now, let's review.

Decibels are logarithmic numbers, so we must understand the lo-________________ to understand the decibel.

### garithm

58

## The log of 1000 is ______.

### 3

59

## The log of 100 is ______.

### 2

60

## The log of 10 is ______.

### 1

61

## The log of 1 is ______.

### 0

62

## The log of _________ is 3.

### 1,000

63

## The log of _________ is 2.

### 100

64

## The log of _________ is 1.

### 10

65

## The log of _________ is 0.

### 1

66

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

### log

67

### log

68

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

### 20

69

## Number of dB = 20 x log __________.

### P1/P2

70

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

### zero

71

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

### zero

72

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

### 1

73

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

### P2

74

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

### cm²

75

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

### 2 dynes/cm²

76