Precalculus: Mathematics for Calculus - 6th Edition

6th Edition

ISBN: 9780840068071

Author: Stewart, James, Redlin, Lothar, Watson, Saleem

Publisher: Cengage Learning

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Textbook Question

Chapter 5.6, Problem 28E

FM Radio Signals The carrier wave for an FM radio signal is modeled by the function

$y = a sin ( 2 π ( 9.15 × 10 7 ) t )$

where t is measured in seconds. Find the period and frequency of the carrier wave.

Expert Solution & Answer

To determine

The value of Period, frequency for a carrier wave.

Answer to Problem 28E

The frequency and period of a carrier wave is $9.15×107$ and $1.09×10−8s$ .

Explanation of Solution

Given:

The function for the carrier wave for an FM radio is,

$y=asin(2π(9.15×)107)t$ (1)

Where,

t is in seconds.

Calculation:

The function for the simple harmonic motion which describes the displacement y of an object at time t is,

$y=Asinωt$ (2)

Compare the equation (1) and equation (2),

The values obtained are A is a and the values of $ω$ is $2π(9.15×)107$ .

Now, calculate the value of period,

The formula for period is,

$p=2πω$ (3)

Substitute the values A for a and $2π(9.15×)107$ for $ω$ in equation (3),

$p=2π2π(9.15×)107=1.09×10−8s$

Thus, the period for the carrier wave of a FM radio is $1.09×10−8s$ .

Frequency is calculated by,

$f=1p$ (4)

Where,

f is frequency of the object.

p is the period of the object.

Substitute $1.09×10−8s$ for p in equation (4),

$f=11.09×10−8=9.15×107$

Thus the value of frequency is $9.15×107$ .

Chapter 5.6, Problem 27E

Chapter 5.6, Problem 29E

Chapter 5 Solutions

Precalculus: Mathematics for Calculus - 6th Edition

Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E Ch. 5.1 - Prob. 6E Ch. 5.1 - Prob. 7E Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E

Ch. 5.1 - Prob. 11E Ch. 5.1 - Prob. 12E Ch. 5.1 - Prob. 13E Ch. 5.1 - Prob. 14E Ch. 5.1 - Prob. 15E Ch. 5.1 - Prob. 16E Ch. 5.1 - Prob. 17E Ch. 5.1 - Prob. 18E Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - Prob. 23E Ch. 5.1 - Prob. 24E Ch. 5.1 - Prob. 25E Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - Prob. 29E Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - Prob. 32E Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Prob. 35E Ch. 5.1 - Prob. 36E Ch. 5.1 - Prob. 37E Ch. 5.1 - Prob. 38E Ch. 5.1 - Prob. 39E Ch. 5.1 - Prob. 40E Ch. 5.1 - Prob. 41E Ch. 5.1 - Prob. 42E Ch. 5.1 - Prob. 43E Ch. 5.1 - Prob. 44E Ch. 5.1 - Prob. 45E Ch. 5.1 - Prob. 46E Ch. 5.1 - Prob. 47E Ch. 5.1 - Prob. 48E Ch. 5.1 - Prob. 49E Ch. 5.1 - Prob. 50E Ch. 5.1 - Prob. 51E Ch. 5.1 - Prob. 52E Ch. 5.1 - Prob. 53E Ch. 5.1 - Prob. 54E Ch. 5.1 - Prob. 55E Ch. 5.1 - Prob. 56E Ch. 5.1 - Prob. 57E Ch. 5.1 - Prob. 58E Ch. 5.2 - Let P(x, y) be the terminal point on the unit...Ch. 5.2 - 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FM Radio Signals The carrier wave for an FM radio signal is modeled by the function y = a sin ( 2 π ( 9.15 × 10 7 ) t ) where t is measured in seconds. Find the period and frequency of the carrier wave.

Solution Summary: The author explains the frequency and period of a carrier wave for an FM radio.

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Answer to Problem 28E

Explanation of Solution

Chapter 5 Solutions