Write the Word or Phrase That Best Completes Each Statement $$f ( t ) = \sin ( 10 t ) \sin ( t )$$

question 170

Essay

Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
-A product of two oscillations with different frequencies such as
$$f ( t ) = \sin ( 10 t ) \sin ( t )$$
is important in acoustics. The result is an oscillation with "oscillating amplitude."
(i) Writethe product $\mathrm { f } ( \mathrm { t } )$ of the two oscillations as a sum of two cosines and call it $\mathrm { g } ( \mathrm { t } )$ .
(ii) Usinga graphing utility, graph the function $g ( t )$ on the interval $0 \leq t \leq 2 \pi$ .
(iii) On the same system as your graph, graph $y = \sin t$ and $y = - \sin t$ .
(iv) Thelast two functions constitute an "envelope" for the function $g ( t )$ . For certain values of t, the two cosine functions in $g ( t )$ cancel each other out and near-silence occurs; between these values, the two functions combine in varying degrees. The phenomenon is known (and heard) as "beats." For what values of t do the functions cancel each other?

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Definitions:

Positions of Power

Roles or statuses within a society, organization, or group that grant individuals authority, influence, and the ability to make decisions that affect others' lives or operations.

Like Themselves

An inclination towards connecting with or favoring individuals who share similar traits, characteristics, or interests; related to the concept of homophily.

Glass Ceiling

A metaphorical barrier that prevents minority groups, including women and people of color, from advancing beyond a certain level in a hierarchical organization due to discrimination.

Women of Color

Refers to women who are not of white or European heritage, emphasizing the intersection of gender and racial or ethnic identity.