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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

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

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

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

0.0002 dynes/cm²