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Hearing Lab 2
The Decibel (Noncadaver Lab)
To the Instructor:
This lab is ideally an in-class lab, as you will want to be free to roam around the room giving
assistance. I’ve found that students respond very well to this activity, because it gives them a
chance to “touch the beast” without pain. You’ll want to warn them to bring a calculator that has
logarithm functions, if they have one. Small groups work well.
Name ____________________________ Course ______________________________
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Hearing Lab 2
The Decibel (Noncadaver Lab)
Today’s lab involves practice working with exponents, logarithms, and, finally, figuring the decibel.
You will work in groups of four or five to go through the problems. DO NOT copy the work of
someone else; instead, seek out explanation when you don’t understand how to complete an item.
I want you to talk and discuss among yourselves, but I want each of you to have the experience
of working through the problems (which, by the way, represent questions on the next test!).
I. Exponents and Logarithms
If you are comfortable with exponents and logarithms, go directly to the section marked
“FIGURING EXPONENTS AND LOGARITHMS” and do the problems there. Otherwise,
continue reading.
An exponent is the power to which a number is raised. For instance, 2 is the exponent in 42 (4
squared, which is 4 X 4, which is equal to 16).
The exponent tells the number of times you will multiply an item by itself:
32 = 3 X 3 = 9
42 = 4 X 4 = 16
33 = 3 X 3 X 3 = 27
53 = 5 X 5 X 5 = 125
1. What are the exponents in the following expressions? What does each expression equal?
Exponent
Answer
42
=
23
=
33
=
46
=
103
=
102
=
105
=
101
=
Logarithms (logs) are exponents. (In our work we’ll only talk about logarithms in base 10, so
relax. It will be presented as Log10, which means to take the base 10 logarithm of a number.)
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So, the Log10 of 1,000 = 3: That is, the “exponent for 10” to give 1,000 is 3. Or, you could say,
“the power to which I must raise 10 to get 1,000 is 3.”
2. Figure the Log10 values for the following:
Log10 (1,000) = _______________
Log10 (10,000) = ______________
Log10 (100) = _________________
Log10 (1,000,000) = ____________
Log10 (100,000) = ______________
Log10 (10,000,000) = ____________
By now you should see that if the exponent is a whole number, the Log10 will be the number of
zeroes after the “1.”
3. Figure a few more:
Log10 (10,000,000) = __________________
Log10 (100,000,000) = _________________
Log10 (10) = _________________________
If you have a logarithm key on your calculator, you’re all set. Here is the keystroke sequence to
get Log10 (1,000) using a Hewlett-Packard calculator:
1000 <enter>
[g] LOG
answer = 3
If your calculator does not have a logarithm key, you may count zeroes.
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Copyright ©2014 Delmar, Cengage Learning. All Rights Reserved.
Figuring Exponents and Logarithms
1. What are the exponents in the following?
22
94
34
63
610
101
75
412
81
156
2. Determine the logarithms (Log10) in the following statements:
Log10 (1,000) = ________________
Log10 (10) = __________________
Log10 (100) = _________________
Log10 (1,000,000) = _____________
Log10 (100,000) = ______________
Log10 (10,000) = ________________
STOP AT THIS POINT AND WAIT FOR THE REST OF YOUR TEAM TO COMPLETE
THE ABOVE SECTION.
II. dB SPL Problems
Figure dB SPL in the following examples. If you have a calculator that will figure logarithms,
this could be fun. If your group doesn’t have a calculator, do those that are marked “no
calculator” until you can flag me down and I’ll loan you mine.
Note: If your calculator only calculates natural logarithms (Ln), then simply multiply the result
times .4343; that is, Log10 = Ln X .4343
Example for figuring dB SPL
dB SPL = 20 Log10 (pressure output/pressure ref)
Given a pressure output = 2,000,000 uPa
1. (No calculator) Given pressure output = 200 uPa, figure dB SPL.
STOP AT THIS POINT AND WAIT FOR THE REST OF YOUR TEAM TO COMPLETE
THE ABOVE SECTION.
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SPL: More Complex Examples
Example: Given 12,000,000 uPa as output, figure dB SPL.
X dB SPL = 20 Log10 (pressure out/pressure ref)
= 20 Log10 (12,000,000 uPa/20 uPa)
= 20 Log10 (600,000)
= 20 X 5.778
= 115.56 dB SPL
1. (Calculator) Figure dB SPL with pressure out = 346,000 uPa.
5. (Calculator) Figure dB SPL with output pressure = 486,000 uPa.
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Copyright ©2014 Delmar, Cengage Learning. All Rights Reserved.
8. (No calculator) Output = 2,000 uPa, figure dB SPL.
STOP AT THIS POINT AND WAIT FOR THE REST OF YOUR TEAM TO COMPLETE
THE ABOVE SECTION.
III. dB Increase and Decrease
dB increase and decrease is a really useful thing to learn (e.g., for reading from an oscilloscope trace)!
Example: You measure a sine wave = 3 V, zero-to-peak.
After raising the volume control (or lowering attenuation), you measure the output voltage to be 96 V.
What is the change in dB?
X dB = 20 Log10 (volts output/volts reference)
= 20 Log10 (96 V/3 V)
= 20 Log10 (32 V)
= 20 (1.505)
= 30.1 dB re: 3 V reference (or dB increase)
So if your original signal was 10 dB SPL, this new output signal is 40 dB SPL (assuming a
perfect world).
1. Given an initial reading of 11.3 V (your reference), you raise the sound output and get a
reading of 431 V. What is the dB change?
2. Given an initial reading of 640 V, you turn the loudness control down and get an output of 21
V. How many dB did you drop? (Hint: The answer is 29.68-dB change.)
3. You measure a sine wave from an audiometer. The dial says 20 dB (which you know is HL),
and you read a voltage on your oscilloscope of 46 V at 20 dB. What is the voltage if you turn
the audiometer up by 6 dB? (Hint: Remember that voltage is the correlate of pressure. What
happens to dB when you double the pressure?)
4. Your initial voltage is 3 V. You increase the volume control and now read 300 V. What is the
dB difference?
5. You turn on the radio and measure .006 V. After cranking the volume up until it parts your
hair, you measure output as 600 V. How many dB have you increased the signal?
6. Your upstairs neighbor has his stereo set to a mind-boggling level. After verbally assaulting
him, you slap an oscilloscope on the speaker leads and get a reading of 43 V. After he turns it
down (under protest), it reads .00043 V. How many dB did you drop the intensity? (Hint: 43 V
is your reference.)
FINISHED!!
THAT WASN’T SO BAD, WAS IT?
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Answer Key
To the Instructor:
The answer key provides the correct responses to Hearing Lab 2: The Decibel. The correct
answers are in bold.
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I. Exponents and Logarithms
1. What are the exponents in the following expressions? What does each expression equal?
Exponent
Answer
42 2
= 16
23 3
= 9
33 3
= 27
46 6
= 4,096
103 3
= 1,000
102 2
= 100
105 5
= 100,000
101 1
= 10
2. Figure the Log10 values for the following:
Log10 (1,000) = 3
Log10 (10,000) = 4
Log10 (100) = 2
Log10 (1,000,000) = 6
Log10 (100,000) = 5
Log10 (10,000,000) = 7
3. Figure a few more:
Log10 (10,000,000) = 7
Log10 (100,000,000) = 8
Log10 (10) = 1
Figuring Exponents and Logarithms
1. What are the exponents in the following?
22
94
34
63
610
101
75
412
81
156
2. Determine the logarithms (Log10) in the following statements:
Log10 (1,000) = 3
Log10 (10) = 1
Log10 (100) = 2
Log10 (1,000,000) = 6
Log10 (100,000) = 5
Log10 (10,000) = 4
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II. dB SPL Problems
1. (No calculator) Given pressure output = 200 uPa, figure dB SPL.
2. (No calculator) Given pressure output = 2,000 uPa, figure dB SPL.
dB SPL = 20 Log10 (2,000 uPa/20 uPa)
= 20 Log10 (100)
3. (No calculator) Given pressure output = 20,000 uPa, figure dB SPL.
dB SPL = 20 Log10 (20,000 uPa/20 uPa)
= 20 Log10 (1,000)
4. Given pressure output = 200,000,000 uPa, figure dB SPL.
SPL: More Complex Examples
1. (Calculator) Figure dB SPL with pressure out = 346,000 uPa.
= 20 Log10 (346,000 uPa/20 uPa)
2. (No calculator) Figure dB SPL with pressure out = 200,000 uPa.
3. (Calculator) Figure dB SPL with pressure out = 25,000 uPa.
= 20 Log10 (25,000 uPa/20 uPa)
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4. (No calculator) Figure dB SPL with pressure out = 20,000 uPa.
= 20 Log10 (20,000 uPa/20 uPa)
5. (Calculator) Figure dB SPL with output pressure = 486,000 uPa.
= 20 Log10 (486,000 uPa/20 uPa)
6. (No calculator) Figure dB SPL with output pressure = 2,000,000 uPa.
= 20 Log10 (2,000,000 uPa/20 uPa)
7. (Calculator) Output = 17,022 uPa, figure dB SPL.
= 20 Log10 (17,022 uPa/20 uPa)
8. (No calculator) Output = 2,000 uPa, figure dB SPL.
= 20 Log10 (2,000 uPa/20 uPa)
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III. dB Increase and Decrease
1. Given an initial reading of 11.3 V (your reference), you raise the sound output and get a
reading of 431 V. What is the dB change?
2. Given an initial reading of 640 V, you turn the loudness control down and get an output of 21
V. How many dB did you drop? (Hint: The answer is 29.68-dB change.)
X dB = 20 Log10 (21 V/640 V)
3. You measure a sine wave from an audiometer. The dial says 20 dB (which you know is HL),
and you read a voltage on your oscilloscope of 46 V at 20 dB. What is the voltage if you turn
the audiometer up 6 dB? (Hint: Remember that voltage is the correlate of pressure. What
happens to dB when you double the pressure?)
4. Your initial voltage is 3 V. You increase the volume control and now read 300 V. What is the
dB difference?
X dB = 20 Log10 (300 V/3 V)
5. You turn on the radio and measure .006 V. After cranking the volume up until it parts your
hair, you measure output as 600 V. How many dB have you increased the signal?
X dB = 20 Log10 (600 V/.006 V)
6. Your upstairs neighbor has his stereo set to a mind-boggling level. After verbally assaulting
him, you slap an oscilloscope on the speaker leads and get a reading of 43 V. After he turns it
down (under protest), it reads .00043 V. How many dB did you drop the intensity? (Hint: 43 V
is your reference.)
X dB = 20 Log10 (.00043 V/43 V)
= 20 Log10 (10,000 V)