Question

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?

• A. \( \frac{1}{4} \) S
• B. \( \frac{1}{8} \) S
• C. \( \frac{1}{2} \) S
• D. \( \frac{1}{16} \) S

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.