The equation of a progressive wave is Y = 3 s | vedclass

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(A) The standard equation of a progressive wave is $Y = A \sin \left( \omega t - kx + \phi \right)$.Comparing the given equation $Y = 3 \sin \left[ \p

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Wavelength $= 10 \ m$

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(A) The standard equation of a progressive wave is $Y = A \sin \left( \omega t - kx + \phi \right)$.Comparing the given equation $Y = 3 \sin \left[ \pi \left( \frac{t}{3} - \frac{x}{5} \right) + \frac{\pi}{4} \right]$ with the standard form:$Y = 3 \sin \left( \frac{\pi t}{3} - \frac{\pi x}{5} + \frac{\pi}{4} \right)$.Here,the amplitude $A = 3 \ m$ (since $x$ and $y$ are in meters).The angular frequency $\omega = \frac{\pi}{3} \ rad/s$.The wave number $k = \frac{\pi}{5} \ rad/m$.$1$. Wavelength $\lambda = \frac{2\pi}{k} = \frac{2\pi}{\pi/5} = 10 \ m$.$2$. Velocity $v = \frac{\omega}{k} = \frac{\pi/3}{\pi/5} = \frac{5}{3} \approx 1.67 \ m/s$.$3$. Frequency $f = \frac{\omega}{2\pi} = \frac{\pi/3}{2\pi} = \frac{1}{6} \approx 0.167 \ Hz$.Comparing these results with the options,option $A$ is correct.

The equation of a progressive wave is $Y = 3 \sin \left[ \pi \left( \frac{t}{3} - \frac{x}{5} \right) + \frac{\pi}{4} \right]$ where $x$ and $y$ are in meters and time $t$ is in seconds. Which of the following is correct?

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