The equation of a progressive wave is y = 8 s | vedclass

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(A) The standard equation of a progressive wave is given by $y = A \sin (\omega t - kx + \phi)$.Comparing this with the given equation $y = 8 \sin \le

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$8$

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(A) The standard equation of a progressive wave is given by $y = A \sin (\omega t - kx + \phi)$.Comparing this with the given equation $y = 8 \sin \left[ \pi \left( \frac{t}{10} - \frac{x}{4} ight) + \frac{\pi}{3} ight]$,we can rewrite it as $y = 8 \sin \left( \frac{\pi t}{10} - \frac{\pi x}{4} + \frac{\pi}{3} ight)$.The wave number $k$ is the coefficient of $x$,which is $k = \frac{\pi}{4}$.We know that the relationship between wave number $k$ and wavelength $\lambda$ is $k = \frac{2\pi}{\lambda}$.Substituting the value of $k$: $\frac{\pi}{4} = \frac{2\pi}{\lambda}$.Solving for $\lambda$: $\lambda = 2 	imes 4 = 8 \, m$.

The equation of a progressive wave is $y = 8 \sin \left[ \pi \left( \frac{t}{10} - \frac{x}{4} \right) + \frac{\pi}{3} \right]$. The wavelength of the wave is .... $m$.

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