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  • One end of a taut string of length 4 m along the Y-axis is fined at x=0. The speed of the waves in the string is  300 m/sThe other end of the string is vibrating in the Y - direction so that s

One end of a taut string of length 4 m along the Y-axis is fined at x=0. The speed of the waves in the string is  300 m/sThe other end of the string is vibrating in the Y - direction so that stationary waves are set up in the string. The Possible waveform of these stationary wave


 

Option: 1

y(t)=A \sin \frac{\pi}{8} x\,\,\, \cos \frac{75 \pi}{2} t \\


Option: 2

y(t)=A \sin \frac{\pi}{6} x\,\,\, \cos \frac{74 \pi}{2} t \\


Option: 3

y(t)=A \sin \frac{\pi}{4} x\,\,\, \cos \frac{70 \pi}{2} t \\


Option: 4

y(t)=A \sin \frac{\pi}{2} x\,\,\, \cos \frac{76 \pi}{2} t \\


Answers (1)

best_answer

K=\frac{2 \pi}{\lambda}=\frac{2 \pi}{4 l} \quad \,\,\,l=\frac{\lambda}{4} \quad \lambda=4 l \\

l=4 \mathrm{~m} \\

K=\frac{2 \pi}{4 \times 4}=\frac{\pi}{8} \\

\frac{w}{K}=300 \mathrm{~m} / \mathrm{s} \\

\frac{w}{\frac{\pi}{8}}=300 \\

\frac{8 \omega}{\pi}=\frac{3 00}{1} \\

8 \omega=300 \pi \\

\omega=\frac{300 \pi}{8}=\frac{75 \pi}{2} \\
y(t)=A \sin \frac{\pi}{8} x\,\,\, \cos \frac{75 \pi}{2} t \\

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Ritika Jonwal

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