Mid -Term 2 Flashcards
In order to study something about the deci____, we must first review some information about the logarithm.
bel
Logarithms are simply exponents, and you know what an exponent is: In the expression 10² = 100, 2 is an _______.
exponent
We have already said that a logarithm is an _______.
exponent
Therefore, the number 2 in the expression 10² is both an exponent and a _______.
logarithm
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
Thus 10³ means the number 10 taken _____ times or
10 x 10 x 10= 1000.
3
In the expression 10³ , the number 10 is called the base, and the number _____ is the exponent or logarithm.
3
In the expression 4³ and 10³, the exponent is 3 in each case, but the base is _______ and 10 respectively.
4
In the expression 10⁵ we mean take 10 ________ times as in 10 x 10 x 10 x 10 x 10 = 100,000.
5
Thus, 10³= _________.
1000
While 10⁵ = ____________.
10000
The logarithm in the expression 10⁵ is the number _______, while the base is the number _________.
5, 10
In dealing with _______bels, the logarithm (or log) to which we refer, will always have a base of 10.
deci
Thus, we can answer, 10² = 100 is the same as the log of 100 is___.
2
10³ = 1,000 or the _________ of 1,000 is 3.
log
The log of 1,000 is _____.
3
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
10³ is the number one followed by 3 _______.
zeros
Thus it is orderly the 10¹ is the number one with __________ zero, or the number 10.
one
It remains orderly when we say, therefore, that 10⁰ = 1, because we are saying 10⁰ equals the number one with _______ zeros following.
no
10⁰ = ______.
1
The logarithm of 1 is _______.
0
Note again the ________________ of 1 is zero.
logarithm
The log of 1,000 = _________.
3
The log of 100 = _________.
2
The log of 1 = ________.
zero
The log of _________ = zero.
1
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
If we divide .002 by .002 we still get _________.
1
If we divide .002 by _________ we still get 1
.002
Regardless of which numbers we choose, if you divide a number by itself, you will always get _______.
1
If you divide .002 by .0002 you get 10. Thus .002/.0002 = _____.
10
If you divide .02 by .0002 you get 100. Thus, .02/.0002 = ______.
100
But if you divide .0002 by _________ you get 1.
.0002
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.
P₁ = the output of the speaker or earphones in units of _________________.
pressure
P₂ = Our __________________ chosen reference level in units of pressure.
arbitrarily
P₂ = Our arbitrarily chosen __________________ level in units of pressure.
reference
To solve the equation we first find the numerical value of the ratio expressed by P₁ over _________.
P2
Then we find the loga-__________ of that value.
rithm
Then we multiply the resulting expression by _________.
20
Note that first we must find the numerical value of the ____________ expressed by P₁ over P₂ .
ratio
Once we have found the numerical value of the ratio, we must then find the ________________ of the numerical value.
logarithm
Once we have the logarithm of the ratio we _______________ it by 20.
multiply
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
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
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
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
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
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
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
Sound Pressure Level is often abbreviated S. P. ____.
L.
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
A sound given at 40dB ___ PL has as its reference point, 0.0002 dyne per square centimeter.
S
A sound given at 55dB SPL has as its reference point ________ dyne/cm² .
0.0002
Thus, the abbreviation ________ means specifically sound pressure level, and usually implies that the reference point of 0 decibels is ______________________.
SPL, 0.0002 dynes/cm²
Now, let’s review.
Decibels are logarithmic numbers, so we must understand the lo-________________ to understand the decibel.
garithm
The log of 1000 is ______.
3
The log of 100 is ______.
2
The log of 10 is ______.
1
The log of 1 is ______.
0
The log of _________ is 3.
1,000
The log of _________ is 2.
100
The log of _________ is 1.
10
The log of _________ is 0.
1
When we use a pressure reference the equation for determining the number of decibels reads: No. dB = 20 x ________ P₁/P₂.
log
When we use a pressure reference the equation for determining the number of decibels reads: No. dB = 20 x ________ P₁/P₂.
log
No. dB = _______ x log P₁/P₂ where P₂ is pressure reference.
20
Number of dB = 20 x log __________.
P1/P2
When P₁ over P₂ is equal to 1, we have a log value of ___________.
zero
With a value of zero in the equation, the number of dB is also ________.
zero
Therefore, 0 dB is obtained when P₁ equals P₂, or when the ratio is ___________.
1
Thus zero dB does not mean silence, or no sound; it means P₁ = ________.
P2
In the measurement of sound pressure level, P₂ is often arbitrarily set at 0.0002 dyne/______.
cm²
A common arbitrary reference point from which to make measurements of sound pressure is 0.000_________________.
2 dynes/cm²
The common reference point from which we make measurements of sound pressure is ______________________.
0.0002 dynes/cm²
