Solve the problem.
-An experiment in a wind tunnel generates cyclic waves. The following data is collected for 52 seconds: $$\begin{array} { c | c }
\begin{array} { c }
\text { Time } \
\text { (in seconds)(in feet per second }
\end{array} & \begin{array} { c }
\text { Wind speed } \
\text { fin }
\end{array} \
\hline 0 & 16 \
\hline 13 & 38 \
\hline 26 & 60 \
\hline 39 & 38 \
\hline 52 & 16
\end{array}$$ Let 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.
A) $V = 22 \sin \left( \frac { \pi } { 26 } t - \frac { \pi } { 2 } \right) + 38$
B) $V = 44 \sin ( 52 t - 26 ) + 22$
C) $V = 60 \sin \left( \frac { \pi } { 26 } t - \frac { \pi } { 2 } \right) + 16$
D) $V = 60 \sin ( 52 t - 26 ) + 16$

Question

Solve the problem.
-An experiment in a wind tunnel generates cyclic waves. The following data is collected for 52 seconds: $$\begin{array} { c | c } 
\begin{array} { c } 
\text { Time } \
\text { (in seconds)(in feet per second }
\end{array} & \begin{array} { c } 
\text { Wind speed } \
\text { fin }
\end{array} \
\hline 0 & 16 \
\hline 13 & 38 \
\hline 26 & 60 \
\hline 39 & 38 \
\hline 52 & 16
\end{array}$$ Let 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. 
A) $V = 22 \sin \left( \frac { \pi } { 26 } t - \frac { \pi } { 2 } \right) + 38$
B) $V = 44 \sin ( 52 t - 26 ) + 22$
C) $V = 60 \sin \left( \frac { \pi } { 26 } t - \frac { \pi } { 2 } \right) + 16$
D) $V = 60 \sin ( 52 t - 26 ) + 16$

Quizplus · Accepted Answer

The sine equation that describes the wave is $V = 22 \sin \left( \frac { \pi } { 26 } t - \frac { \pi } { 2 } \right) + 38$. This is because the amplitude of the wave is half the difference between the maximum and minimum wind speeds (60 - 16)/2 = 22, the period is the total time for one complete cycle (52 seconds), which gives a frequency of $\frac{\pi}{26}$ when considering $2\pi$ radians for a full sine wave cycle, and the vertical shift is the average of the maximum and minimum speeds (60 + 16)/2 = 38. The phase shift aligns the wave with the given data points.

Solve the Problem Let V Represent the Wind Speed (Velocity) in Feet Per