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(B) The given equation of the stationary wave is $y = \sin(2\pi x) \cos(2\pi t)$.Comparing this with the standard equation of a stationary wave $y = A

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$0.5$

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(B) The given equation of the stationary wave is $y = \sin(2\pi x) \cos(2\pi t)$.Comparing this with the standard equation of a stationary wave $y = A \sin(\frac{2\pi x}{\lambda}) \cos(\omega t)$,we get $\frac{2\pi x}{\lambda} = 2\pi x$.This implies $\frac{2\pi}{\lambda} = 2\pi$,so $\lambda = 1 	ext{ m}$.The minimum length of the string corresponds to the fundamental mode (first harmonic),where the length $L$ is equal to half the wavelength.Therefore,$L_{\min} = \frac{\lambda}{2} = \frac{1}{2} 	ext{ m} = 0.5 	ext{ m}$.

$A$ string is rigidly tied at two ends and its equation of vibration is given by $y = \sin(2\pi x) \cos(2\pi t)$. Then the minimum length of the string is .... $m$

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