Solve the problem.
-An experiment in a wind tunnel generates cyclic waves. The following data is collected for 36 seconds: $$\begin{array} { c | c }
\begin{array} { c }
\text { Time } \
\text { (in seconds) }
\end{array} & \begin{array} { c }
\text { Wind speed } \
\text { (in feet per second) }
\end{array} \
\hline 0 & 16 \
\hline 9 & 40 \
\hline 18 & 64 \
\hline 27 & 40 \
\hline 36 & 16
\end{array}$$ Let $\mathrm { V }$ represent the wind speed (velocity) in feet per second and let $t$ represent the time in seconds. Write a sine equation that describes the wave.

Question

Solve the problem.
-An experiment in a wind tunnel generates cyclic waves. The following data is collected for 36 seconds: $$\begin{array} { c | c } 
\begin{array} { c } 
\text { Time } \
\text { (in seconds) }
\end{array} & \begin{array} { c } 
\text { Wind speed } \
\text { (in feet per second) }
\end{array} \
\hline 0 & 16 \
\hline 9 & 40 \
\hline 18 & 64 \
\hline 27 & 40 \
\hline 36 & 16
\end{array}$$ Let $\mathrm { V }$ represent the wind speed (velocity) in feet per second and let $t$ represent the time in seconds. Write a sine equation that describes the wave.

Quizplus · Accepted Answer

The amplitude of the wave is half the difference between the maximum and minimum wind speeds, which is $\frac{64 - 16}{2} = 24$. The period of the wave is 36 seconds, so the frequency is $\frac{2\pi}{36} = \frac{\pi}{18}$. The wave reaches its first maximum at 9 seconds, so we shift it by $\frac{\pi}{2}$ to the left. The vertical shift is the average of the maximum and minimum speeds, which is $\frac{64 + 16}{2} = 40$. Therefore, the correct equation is $V = 24 \sin \left( \frac { \pi } { 18 } t - \frac { \pi } { 2 } \right) + 40$.

Solve the Problem Let V\mathrm { V }V Represent the Wind Speed (Velocity) in Feet Per Second and Cyclic

Solve the Problem Let $\mathrm { V }$ Represent the Wind Speed (Velocity) in Feet Per Second and Cyclic