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A wave has an amplitude equal to 4.0m, angular speed \(\frac{1}{3} \pi\) rads-1 and phase...

Physics
WAEC 2000

A wave has an amplitude equal to 4.0m, angular speed \(\frac{1}{3} \pi\) rads-1 and phase angle \(\frac{2}{3} \pi\) rad. The displacement y of the wave particle is given as

  • A. y = 4 sin \(\frac{\pi}{3}\)(t + 2)
  • B. y = 4 sin \(\frac{\pi}{3}\)(t + \(\frac{2}{\pi}\)
  • C. y = 4 sin \(\frac{\pi}{3} (2t + 1)\)
  • D. y = 4 sin \(\frac{\pi}{3}\) (t + 1)
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Correct Answer: Option A
Explanation

y = A sin(ωt + Φ )

A = 4cm, Φ = \(\frac{2}{3} \pi \) rad, ω = \(\frac{1}{3}\pi\ rads^{-1}\)

substituting the given values

y = 4 sin ( \(\frac{1}{3}\pi\)t + \(\frac{2}{3} \pi \))

y = 4sin  \(\frac{\pi}{3}\)( t + 2)


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