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(C) Given frequency $f = \frac{1}{8} \, Hz$.Therefore,time period $T = \frac{1}{f} = 8 \, s$.Given wavelength $\lambda = 24 \, m$.The wave speed $v =

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$9$

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(C) Given frequency $f = \frac{1}{8} \, Hz$.Therefore,time period $T = \frac{1}{f} = 8 \, s$.Given wavelength $\lambda = 24 \, m$.The wave speed $v = f \lambda = \frac{1}{8} 	imes 24 = 3 \, m/s$.The time taken by the wave to reach the particle at distance $x = 9 \, m$ is $t_1 = \frac{x}{v} = \frac{9}{3} = 3 \, s$.The particle starts its motion from the mean position (moving up first). To reach the lower extreme for the first time,the particle must complete $\frac{3}{4}$ of its oscillation cycle.The time taken by the particle to reach the lower extreme from the moment the wave reaches it is $t_2 = \frac{3T}{4} = \frac{3}{4} 	imes 8 = 6 \, s$.Total time taken = $t_1 + t_2 = 3 \, s + 6 \, s = 9 \, s$.

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