ExamBro
ExamBro
KCET · Physics · Waves and Sound

The equation of a wave is given by \(y=10 \sin \left(\frac{2 \pi}{45} t+\alpha\right)\). If the displacement is \(5 \mathrm{~cm}\) at \(t=0\), then the total phase at \(t=7.5 \mathrm{~s}\) is

  1. A \(\frac{\pi}{3}\)
  2. B \(\frac{\pi}{2}\)
  3. C \(\frac{\pi}{6}\)
  4. D \(\pi\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{\pi}{2}\)

Step-by-step Solution

Detailed explanation

\(y=10 \sin \left[\frac{2 \pi}{45} t+\alpha\right]\)
\(y=5 \mathrm{~cm}\) at \(t=0\)
\(\therefore \quad 5=10(\sin \alpha)\)
or
\(\sin \alpha=\frac{1}{2}\)
or
\(\alpha=\frac{\pi}{6}\)
Again if \(t=7.5 \mathrm{~s}\)
Then total phase \(=\frac{2 \pi}{45} \times \frac{15}{2}+\frac{\pi}{6}\)
\(=\frac{\pi}{3}+\frac{\pi}{6}\)
\(=\frac{2 \pi+\pi}{6}=\frac{3 \pi}{6}=\frac{\pi}{2}\)