The equation of a wave travelling in a string | vedclass

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(B) The standard equation of a travelling wave is given by $y = a \cos(\omega t - kx)$.Comparing the given equation $y = 3 \cos \pi(100t - x)$ with th

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$2$

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(B) The standard equation of a travelling wave is given by $y = a \cos(\omega t - kx)$.Comparing the given equation $y = 3 \cos \pi(100t - x)$ with the standard form,we rewrite it as $y = 3 \cos(100\pi t - \pi x)$.Here,the wave number $k$ is the coefficient of $x$,so $k = \pi$.We know that the relationship between wave number $k$ and wavelength $\lambda$ is $k = \frac{2\pi}{\lambda}$.Substituting the value of $k$,we get $\pi = \frac{2\pi}{\lambda}$.Solving for $\lambda$,we find $\lambda = 2 \ cm$.

The equation of a wave travelling in a string can be written as $y = 3\cos \pi (100t - x)$. Its wavelength is .... $cm$.

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