A string is rigidly tied at two ends and its equation of vibration is given by $y = \cos 2\pi \,t\sin \sin \pi x.$ Then minimum length of string is .... $m$
Medium
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(b) Given equation of stationary wave is
$y = \sin 2\pi x\cos 2\pi t$,
$y = \sin 2\pi x\cos 2\pi t$,
comparing it with standard equation $y = 2A\sin \frac{{2\pi x}}{\lambda }\cos \frac{{2\pi x}}{\lambda }$
We have $\frac{{2\pi x}}{\lambda } = 2\pi x$ ==> $\lambda = 1m$
Minimum distance of string (first mode) ${L_{\min }}\, = \frac{\lambda }{2} = \frac{1}{2}m$
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