Calculus: Graphical, Numerical, Algebraic

3rd Edition

ISBN: 9780133688399

Author: Finney, Ross L.

Publisher: Pearson/Prentice Hall

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Question

Chapter 1.6, Problem 23E

(a)

To determine

To find:The sinusoidal regressionequation for the given data and its graph on a scatter plot.

(a)

Expert Solution

Answer to Problem 23E

The sinusoidal regression equation for the given data is y=1.543sin(2468.635x−0.494)+0.438 and its graph is shown in Figure (1).

Explanation of Solution

Given information:The table given below shows the Turning Fork data.

Calculus: Graphical, Numerical, Algebraic, Chapter 1.6, Problem 23E , additional homework tip 1

Calculation:

To find the sinusoidal regression equation of the given data, use graphing calculator.

Step 1: Press STAT1 keys to enter the given data.

Step 2: List the values for time in the L1 column and values for pressure in the L2 column.

Step 3: Press the keystrokes STAT⇒ALPHAPRGMENTER to find line of sinusoidal regression and again press ENTER key.

y=1.543sin(2468.635x−0.494)+0.438

Step 1: Press 2ndY= and make sure that Plot 1 is ON. Choose the scatter plot icon in type.

Step 2: Press Y= and write the left hand side of the equation y=1.543sin(2468.635x−0.494)+0.438 after the symbol Y1 .

Step 3: Set the window at [0, 0.01] by [−2.5, 2.5] . Press the GRAPH key to produce the graph as shown below.

Calculus: Graphical, Numerical, Algebraic, Chapter 1.6, Problem 23E , additional homework tip 2

Figure (1)

Therefore, the sinusoidal regression equation for the given data is y=1.543sin(2468.635x−0.494)+0.438 and its graph is shown in Figure (1).

(c)

To determine

To find: The frequency and the musical note produced by the turning fork.

(c)

Expert Solution

Answer to Problem 23E

The required frequency is 392.9 Hz and the musical not is “G”.

Explanation of Solution

Given information:The table given below shows the frequencies of note.

Note	Frequency (Hz)
C	262
C# or Db	277
D	294
D# or Eb	311
E	330
F	349
F# or Gb	370
G	392
G# or Ab	415
A	440
A# or Bb	466
B	494
C (next octave)	524

Calculation:

From part (a), the sinusoidal regression equation for the given data is y=1.543sin(2468.635x−0.494)+0.438 .

The general equation for the sine function is given by,

y=Asin[2πB(x−C)]+D

On comparing both the equations, the period of the function is:

2πB=2468.6352π2468.635=B

The frequency is the inverse of the period. So,

F=2468.6352π=392.9 Hz

From the table it can be observed the frequency of note “G” is 392 Hz.

Therefore, the required frequency is 392.9 Hz and the musical not is “G”.

Chapter 1.6, Problem 22E

Chapter 1.6, Problem 24E

Chapter 1 Solutions

Calculus: Graphical, Numerical, Algebraic

Ch. 1.1 - Prob. 1QR Ch. 1.1 - Prob. 2QR Ch. 1.1 - Prob. 3QR Ch. 1.1 - Prob. 4QR Ch. 1.1 - Prob. 5QR Ch. 1.1 - Prob. 6QR Ch. 1.1 - Prob. 7QR Ch. 1.1 - Prob. 8QR Ch. 1.1 - Prob. 9QR Ch. 1.1 - Prob. 10QR

Ch. 1.1 - Prob. 1E Ch. 1.1 - Prob. 2E Ch. 1.1 - Prob. 3E Ch. 1.1 - Prob. 4E Ch. 1.1 - Prob. 5E Ch. 1.1 - Prob. 6E Ch. 1.1 - Prob. 7E Ch. 1.1 - Prob. 8E Ch. 1.1 - Prob. 9E Ch. 1.1 - Prob. 10E Ch. 1.1 - Prob. 11E Ch. 1.1 - Prob. 12E Ch. 1.1 - Prob. 13E Ch. 1.1 - Prob. 14E Ch. 1.1 - Prob. 15E Ch. 1.1 - Prob. 16E Ch. 1.1 - Prob. 17E Ch. 1.1 - Prob. 18E Ch. 1.1 - Prob. 19E Ch. 1.1 - Prob. 20E Ch. 1.1 - Prob. 21E Ch. 1.1 - Prob. 22E Ch. 1.1 - Prob. 23E Ch. 1.1 - Prob. 24E Ch. 1.1 - Prob. 25E Ch. 1.1 - Prob. 26E Ch. 1.1 - Prob. 27E Ch. 1.1 - Prob. 28E Ch. 1.1 - Prob. 29E Ch. 1.1 - Prob. 30E Ch. 1.1 - Prob. 31E Ch. 1.1 - Prob. 32E Ch. 1.1 - Prob. 33E Ch. 1.1 - Prob. 34E Ch. 1.1 - Prob. 35E Ch. 1.1 - Prob. 36E Ch. 1.1 - Prob. 37E Ch. 1.1 - Prob. 38E Ch. 1.1 - Prob. 39E Ch. 1.1 - Prob. 40E Ch. 1.1 - Prob. 41E Ch. 1.1 - Prob. 42E Ch. 1.1 - Prob. 43E Ch. 1.1 - Prob. 44E Ch. 1.1 - Prob. 45E Ch. 1.1 - Prob. 46E Ch. 1.1 - Prob. 47E Ch. 1.1 - Prob. 48E Ch. 1.1 - Prob. 49E Ch. 1.1 - Prob. 50E Ch. 1.1 - 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Prob. 61E Ch. 1.6 - Prob. 62E Ch. 1.6 - Prob. 1QQ Ch. 1.6 - Prob. 2QQ Ch. 1.6 - Prob. 3QQ Ch. 1.6 - Prob. 4QQ Ch. 1 - Prob. 1RE Ch. 1 - Prob. 2RE Ch. 1 - Prob. 3RE Ch. 1 - Prob. 4RE Ch. 1 - Prob. 5RE Ch. 1 - Prob. 6RE Ch. 1 - Prob. 7RE Ch. 1 - Prob. 8RE Ch. 1 - Prob. 9RE Ch. 1 - Prob. 10RE Ch. 1 - Prob. 11RE Ch. 1 - Prob. 12RE Ch. 1 - Prob. 13RE Ch. 1 - Prob. 14RE Ch. 1 - Prob. 15RE Ch. 1 - Prob. 16RE Ch. 1 - Prob. 17RE Ch. 1 - Prob. 18RE Ch. 1 - Prob. 19RE Ch. 1 - Prob. 20RE Ch. 1 - Prob. 21RE Ch. 1 - Prob. 22RE Ch. 1 - Prob. 23RE Ch. 1 - Prob. 24RE Ch. 1 - Prob. 25RE Ch. 1 - Prob. 26RE Ch. 1 - Prob. 27RE Ch. 1 - Prob. 28RE Ch. 1 - Prob. 29RE Ch. 1 - Prob. 30RE Ch. 1 - Prob. 31RE Ch. 1 - Prob. 32RE Ch. 1 - Prob. 33RE Ch. 1 - Prob. 34RE Ch. 1 - Prob. 35RE Ch. 1 - Prob. 36RE Ch. 1 - Prob. 37RE Ch. 1 - Prob. 38RE Ch. 1 - Prob. 39RE Ch. 1 - Prob. 40RE Ch. 1 - Prob. 41RE Ch. 1 - Prob. 42RE Ch. 1 - Prob. 43RE Ch. 1 - Prob. 44RE Ch. 1 - Prob. 45RE Ch. 1 - Prob. 46RE Ch. 1 - Prob. 47RE Ch. 1 - 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The sinusoidal regressionequation for the given data and its graph on a scatter plot .

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To find:The sinusoidal regressionequation for the given data and its graph on a scatter plot.

Answer to Problem 23E

Explanation of Solution

To find: The frequency and the musical note produced by the turning fork.

Answer to Problem 23E

Explanation of Solution

Chapter 1 Solutions

Additional Math Textbook Solutions