A sound wave can be modeled by the function \( y(t) = 0.5 \cos(440 \pi t) \), where \( y(t) \) is the displacement and \( t \) is the time in seconds. Determine the frequency and period of this sound wave. - 3.4 Sine and Cosine Function Graphs - Review - Use this assignment in your class!

You can use this assignment in your class!

Mastery Progress(100.0%)

CLOSE REVIEW

3.4 Sine and Cosine Function Graphs - Review

10.

11.

12.

13.

14.

15.

You answeredJUST NOW

Did you like this question?

(Voting helps us personalize your learning experience!)

Instructor solution

AI InstructorAUG 12, 2024, 11:37:18 AM

Was this helpful?

(Voting helps us personalize your learning experience!)

Think you've got it?

Select one of the following options:

Submit answer

Was this helpful?

(Voting helps us personalize your learning experience!)

Continue review

You may exit out of this review and return later without penalty.

Describe how the amplitude of the function

y = A \sin (x)

affects its graph. Provide an example with a specific value for

A

Explain how the period of the function

y = \cos (B x)

changes with different values of

B

. Provide an example with a specific value for

B

How does a phase shift affect the graph of the function

y = \sin (x - C)

? Provide an example with a specific value for

C

Compare the graphs of

y = \sin (x)

and

y = \sin (x - \frac{π}{3})

. How does the phase shift affect the position of the graph?

How does the graph of

y = 2 \cos (2 x - π)

differ from the graph of

y = \cos (x)

? Discuss the changes in amplitude, period, and phase shift.

A coastal town experiences high tides and low tides every day. The height of the tide can be modeled by the function

h (t) = 3 \sin (\frac{π}{6} t) + 5

, where

h (t)

is the height of the tide in feet and

t

is the time in hours. Explain what the amplitude, period, and vertical shift of this function represent in the context of the tides.

A sound wave can be modeled by the function

y (t) = 0.5 \cos (440 π t)

, where

y (t)

is the displacement and

t

is the time in seconds. Determine the frequency and period of this sound wave.

A Ferris wheel has a diameter of 40 meters and completes one full rotation every 5 minutes. If the height of a seat on the Ferris wheel above the ground can be modeled by a cosine function, write the equation for the height

h (t)

in terms of time

t

in minutes, assuming the lowest point of the Ferris wheel is 2 meters above the ground.

A temperature sensor records the temperature in a room over time and finds that it can be modeled by the function

T (t) = 10 \cos (\frac{π}{12} t) + 25

, where

T (t)

is the temperature in degrees Celsius and

t

is the time in hours. Describe the temperature fluctuations in the room over a 24-hour period.

A pendulum swings back and forth, and its displacement from the equilibrium position can be modeled by the function

d (t) = 5 \sin (2 π t)

, where

d (t)

is the displacement in meters and

t

is the time in seconds. Determine the amplitude, period, and frequency of the pendulum's motion.

A sound wave can be modeled by the function

y (t) = 0.5 \cos (440 π t)

, where

y (t)

is the displacement and

t

is the time in seconds. Determine the frequency and period of this sound wave.

The frequency of the sound wave is 220 Hz, as the coefficient of

t

in the cosine function is

440 π

, which corresponds to

2 π f

. Solving for

f

, we get

f = 220

Hz. The period

T

is the reciprocal of the frequency, so

T = \frac{1}{220}

seconds.

Instructor solution

Think you've got it?

Sharing assignments in OpenClass