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 $g ( \mathrm { t } )$.
(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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The Answer of 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 $g ( \mathrm { t } )$.
(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?

Solve the Problem f(t)=sin⁡(10t)sin⁡(t)f ( t ) = \sin ( 10 t ) \sin ( t )f(t)=sin(10t)sin(t)

Solve the Problem $f ( t ) = \sin ( 10 t ) \sin ( t )$