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Homework 4 Questions for Algebra and Trigonometry I | MA 153, Assignments of Trigonometry

Indiana University-Purdue University-Fort Wayne Trigonometry

Material Type: Assignment; Class: Algebra And Trig I; Subject: Mathematics; University: Indiana University-Purdue University-Fort Wayne; Term: Fall 2006;

Typology: Assignments

Pre 2010

Uploaded on 08/16/2009

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Measurement of Sound Intensity

The decibel was invented by engineers at Bell Telephone as a convenient way to measure sound intensity.

The name is in tribute to the company’s founder Alexander Graham Bell. Suppose L represents loudness

level in decibels and I represents sound intensity. The following table gives several values.

Sound Intensity, I Loudness Level, L

Sound (W/cm2) (dB)

Threshold of hearing 0.0000000000000001 = 10–16 0

Normal breathing 0.000000000000001 = 10–15 10

Quiet library 0.000000000001 = 10–12 40

Busy street traffic 0.000000001 = 10–9 70

Jackhammer (at 2 m) 0.000001 = 10–6 100

Jet plane takeoff (at 30 m) 0.001 = 10–3 130

Rupture of eardrum 1 160

1. Given any value of I, we would like to determine how can we find L.

As a start, create a middle column called X = log I.

Fill in the blanks to complete the third column in the table below.

Sound Loudness

Intensity, I Level, L

Sound (W/cm2) X = log I (dB)

Threshold of hearing 10–16

0

Normal breathing 10–15

10

Quiet library 10–12 40

Busy street traffic 10–9 70

Jackhammer (at 2 m) 10–6 100

Jet plane takeoff (at 30 m) 10–3 130

Rupture of eardrum 1 160

2. Look at the last two columns, X and L. How can you tell that the relationship is linear?

(You might make a column showing

X

∆

and L

∆

and discuss what this tells you.)

3. Suppose L is written as a function of X.

Is this function increasing, decreasing, or constant? _________________

4. If the equation of this function is written in the form L = mX + b, what is the value of m? ______

(This is where the “deci” comes from in the name decibel.) What is the value of b? ______

Before proceeding, check your equation is correct with a grapher by producing a table which matches

the values for X and L above.

(2)

(1)

Name_____________________________

MA 153 Writing Assignment 4 Due Wednesday 10-18-06 (10 pts)

Partial preview of the text

Download Homework 4 Questions for Algebra and Trigonometry I | MA 153 and more Assignments Trigonometry in PDF only on Docsity!

Measurement of Sound Intensity The decibel was invented by engineers at Bell Telephone as a convenient way to measure sound intensity. The name is in tribute to the company’s founder Alexander Graham Bell. Suppose L represents loudness level in decibels and I represents sound intensity. The following table gives several values.

Sound Intensity, I Loudness Level, L Sound (W/cm^2 ) (dB) Threshold of hearing 0.0000000000000001 = 10 –16^0 Normal breathing 0.000000000000001 = 10 –15^10 Quiet library 0.000000000001 = 10–12^40 Busy street traffic 0.000000001 = 10–9^70 Jackhammer (at 2 m) 0.000001 = 10–6^100 Jet plane takeoff (at 30 m) 0.001 = 10–3^130 Rupture of eardrum 1 160

Given any value of I , we would like to determine how can we find L. As a start, create a middle column called X = log I. Fill in the blanks to complete the third column in the table below.

Sound Loudness Intensity , I Level, L Sound (W/cm^2 ) X = log I (dB)

Threshold of hearing 10 –16^0 Normal breathing 10 –15^10 Quiet library 10 –12^40 Busy street traffic 10 –9^70 Jackhammer (at 2 m) 10 –6^100 Jet plane takeoff (at 30 m) 10 –3^130 Rupture of eardrum 1 160

Look at the last two columns, X and L. How can you tell that the relationship is linear? (You might make a column showing ∆ X and ∆ L and discuss what this tells you.)
Suppose L is written as a function of X. Is this function increasing , decreasing , or constant? _________________
If the equation of this function is written in the form L = mX + b , what is the value of m? ______ (This is where the “deci” comes from in the name decibel.) What is the value of b? ______ Before proceeding, check your equation is correct with a grapher by producing a table which matches the values for X and L above.

(2)

(1)

MA 153 Writing Assignment 4 Due Wednesday 10 - 18 -06 (10 pts) Name_____________________________

Select the best choice for your equation.

You have found L in terms of X. Resubstitute X = log I in your equation to write L in terms of I.
If you sit in the front row of a rock concert, its sound intensity is 10 –4^ W/cm^2. What is the loudness level in decibels? ________ Use an equation and show work.

Check that your result is you expect, keeping in mind the table of sound intensity measurements.

The blast of 1 kiloton of T.N.T. is quite loud – about 240 dB. Give its sound intensity in W/cm^2. Show work.
The sound of one Christmas caroler is about 60 dB. Suppose we have 4 carolers, each singing at an intensity which produces a loudness level of 60 decibels. What is the loudness level in decibels, of this quartet? _________ dB (round to 1 decimal place) Hint 1: Use your equation. Hint 2: The sound intensity is quadrupled.
Attach a typed page which addresses the following two items: o What did you learn from this assignment (or chapter 4) that you did not know before? o What questions do you have (if any) concerning concepts about which you are not quite clear? o You have seen what a decibel is. How would you think a Bel would be defined?

A. L = 101 X

B. L = 101 X – 16

C. L = 101 X + 16

D. L = 101 X – 160

E. L = 101 X + 160

K. L = 10 X

L. L = 10 X – 16

M. L = 10 X + 16

N. L = 10 X – 160

O. L = 10 X + 160

F. L = – 101 X

G. L = – 101 X – 16

H. L = – 101 X + 16

I. L = – 101 X – 160

J. L = – 101 X + 160

P. L = –10 X

Q. L = –10 X – 16

R L = –10 X + 16

S. L = –10 X – 160

T. L = –10 X + 160

U. None of these

I L