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CSD 371 > Mid -Term 2 > Flashcards

Mid -Term 2 Flashcards

1
Q

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

A

bel

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2
Q

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

A

exponent

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3
Q

We have already said that a logarithm is an _______.

A

exponent

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4
Q

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

A

logarithm

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5
Q

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.

A

100

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6
Q

Thus 10³ means the number 10 taken _____ times or

10 x 10 x 10= 1000.

A

3

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7
Q

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

A

3

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8
Q

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

A

4

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9
Q

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

A

5

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10
Q

Thus, 10³= _________.

A

1000

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11
Q

While 10⁵ = ____________.

A

10000

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12
Q

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

A

5, 10

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13
Q

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

A

deci

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14
Q

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

A

2

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15
Q

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

A

log

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16
Q

The log of 1,000 is _____.

A

3

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17
Q

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.

A

2

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18
Q

10³ is the number one followed by 3 _______.

A

zeros

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19
Q

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

A

one

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20
Q

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

A

no

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21
Q

10⁰ = ______.

A

1

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22
Q

The logarithm of 1 is _______.

A

0

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23
Q

Note again the ________________ of 1 is zero.

A

logarithm

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24
Q

The log of 1,000 = _________.

A

3

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25
Q

The log of 100 = _________.

A

2

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26
Q

The log of 1 = ________.

A

zero

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27
Q

The log of _________ = zero.

A

1

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28
Q

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 ______.

A

1

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29
Q

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

A

1

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30
Q

If we divide .002 by _________ we still get 1

A

.002

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31
Q

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

A

1

32
Q

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

A

10

33
Q

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

A

100

34
Q

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

A

.0002

35
Q

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.

A
  • 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
Q

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

A

pressure

37
Q

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

A

arbitrarily

38
Q

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

A

reference

39
Q

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

A

P2

40
Q

Then we find the loga-__________ of that value.

A

rithm

41
Q

Then we multiply the resulting expression by _________.

A

20

42
Q

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

A

ratio

43
Q

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

A

logarithm

44
Q

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

A

multiply

45
Q

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 ______________.

A

P2, zero

46
Q

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.

A

equal

47
Q

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.

A

P1, 2, 40

48
Q

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

A

logarithm, 20

49
Q

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 _______.

A

4, 80

50
Q

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.

A

arbitrary

51
Q

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 .

A

pressure, dyne

52
Q

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

A

L.

53
Q

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.

A

2

54
Q

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

A

S

55
Q

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

A

0.0002

56
Q

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

A

SPL, 0.0002 dynes/cm²

57
Q

Now, let’s review.

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

A

garithm

58
Q

The log of 1000 is ______.

A

3

59
Q

The log of 100 is ______.

A

2

60
Q

The log of 10 is ______.

A

1

61
Q

The log of 1 is ______.

A

0

62
Q

The log of _________ is 3.

A

1,000

63
Q

The log of _________ is 2.

A

100

64
Q

The log of _________ is 1.

A

10

65
Q

The log of _________ is 0.

A

1

66
Q

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

A

log

67
Q

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

A

log

68
Q

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

A

20

69
Q

Number of dB = 20 x log __________.

A

P1/P2

70
Q

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

A

zero

71
Q

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

A

zero

72
Q

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

A

1

73
Q

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

A

P2

74
Q

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

A

cm²

75
Q

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

A

2 dynes/cm²

76
Q

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

A

0.0002 dynes/cm²

CSD 371 (2 decks)

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