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  • The equation of a wave is given by <img alt="y=20 \sin \left(\frac{4 \pi}{4s} t+a\right)" src="https://entrancecorner.oncodecogs.com/gif.latex?y%3D20%20%5Csin%20%5Cle

The equation of a wave is given by y=20 \sin \left(\frac{4 \pi}{4s} t+a\right) If the displacement is \mathrm{8} \mathrm{cm} at t=0, then the total phase at t=9.5 \mathrm{~s}

Option: 1

8=30 sin d


Option: 2

8=20 sin d


Option: 3

4=10 sin d


Option: 4

8=20 cos d


Answers (1)

best_answer

The given equation of a wave is

y=20 \sin \left(\frac{4 \pi}{4s} t+d\right) \\

At t=0        y=8cm

\therefore 8=20 \sin d

\sin a=\frac{\not 8}{\not 20} =\frac{2}{5} \\

\sin a=\frac{2}{5} \\

d=\sin ^{-1} \frac{2}{5}

Hence, the total Phase at d=9.5

=\frac{95}{10}=\frac{19}{2} s \\

\varphi=\frac{4 \pi}{4s} \times \frac{19}{2}+d \\

\varphi=\frac{2 \pi \times 19}{4s}+d \\

\varphi=\frac{38 \pi}{45}+\sin ^{-1} \frac{2}{5}\varphi=\frac{38 \pi}{4s}+\sin ^{-1} \frac{2}{5}

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Rishi

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