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MHT CET · Physics · Waves and Sound

The equation of wave is given by \(y=10 \sin \left(\frac{2 \pi t}{30}+\alpha\right)\). If the displacement is \(5 \mathrm{~cm}\) at \(\mathrm{t}=0\), then the total phase angle at \(\mathrm{t}=7.5 \mathrm{~s}\) will be

  1. A \(\frac{\pi}{3} \mathrm{rad}\)
  2. B \(\frac{\pi}{2} \mathrm{rad}\)
  3. C \(\frac{2 \pi}{5} \mathrm{rad}\)
  4. D \(\frac{2 \pi}{3} \mathrm{rad}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{2 \pi}{3} \mathrm{rad}\)

Step-by-step Solution

Detailed explanation

\(\mathrm{y}=10 \sin \left(\frac{2 \pi \mathrm{t}}{30}+\alpha\right)\)
At \(\mathrm{t}=0, \mathrm{y}=5 \mathrm{~cm}\)
\(5=10 \sin \alpha\)
\(\alpha=\frac{\pi}{6}\)
At \(\mathrm{t}=7.5\), the total phase
\(\phi=\frac{2 \pi \times 7.5}{30}+\alpha=\frac{\pi}{2}+\frac{\pi}{6}=\frac{2 \pi}{3} \mathrm{rad}\)