The pattern of standing waves formed on a str | vedclass

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(B) The time period $T$ of the wave is given by $T = \frac{1}{f} = \frac{1}{256} \ s$.The standing wave oscillates between its extreme position (shown

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$10^{-3}$

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(B) The time period $T$ of the wave is given by $T = \frac{1}{f} = \frac{1}{256} \ s$.The standing wave oscillates between its extreme position (shown at $t=0$) and its mean position (where the string is flat,$y=0$ everywhere).The string reaches its mean position at times $t = \frac{T}{4}, \frac{3T}{4}, \frac{5T}{4}, \dots$Calculating these values:$t_1 = \frac{T}{4} = \frac{1}{256 	imes 4} = \frac{1}{1024} \approx 0.976 	imes 10^{-3} \ s \approx 9.8 	imes 10^{-4} \ s$.$t_2 = \frac{3T}{4} = 3 	imes 0.976 	imes 10^{-3} \approx 2.93 	imes 10^{-3} \ s$.$t_3 = \frac{5T}{4} = 5 	imes 0.976 	imes 10^{-3} \approx 4.88 	imes 10^{-3} \ s \approx 4.9 	imes 10^{-3} \ s$.Comparing these with the given options,$10^{-3} \ s$ is not a possible value for the string to be at its mean position.

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