A particle on a string undergoes a transverse wave motion given by:
\[
y = 5 \sin \left( 4 \pi t - \frac{\pi x}{2} \right)
\]
(All quantities in SI units.)How much time does a particle at \( x = 0 \) take to go from mean position to extreme (maximum displacement) for the first time?
Show Hint
The time for a particle to move from the mean position to extreme displacement in a sinusoidal wave is \( \frac{1}{8} \) of the time period, since it reaches the extreme for the first time at \( \frac{\pi}{2} \) radians.