Solve the problem.
-An experiment in a wind tunnel generates cyclic waves. The following data is collected for 52 seconds: $$\begin{array} { c | c }
\text { Time } & \text { Wind speed } \
\text { (in seconds) } & \text { (in feet per second) } \
\hline 0 & 16 \
\hline 13 & 38 \
\hline 26 & 60 \
\hline 39 & 38 \
\hline 52 & 16
\end{array}$$ 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: $$\begin{array} { c | c } 
\text { Time } & \text { Wind speed } \
\text { (in seconds) } & \text { (in feet per second) } \
\hline 0 & 16 \
\hline 13 & 38 \
\hline 26 & 60 \
\hline 39 & 38 \
\hline 52 & 16
\end{array}$$ 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 fits the given data 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 of the wave is 52 seconds, so the frequency is $ \frac { 2\pi } { 52 } = \frac { \pi } { 26 }$. The phase shift is $-\frac{\pi}{2}$ to match the starting point at t=0, and the vertical shift is 38 to center the wave between the maximum and minimum values.

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