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(D) The standard equation of a plane progressive wave is $y = A \cos(\omega t - kx)$.Given equation: $y = 5 \cos(200\pi t - \frac{\pi x}{150})$.Compar

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$300$

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(D) The standard equation of a plane progressive wave is $y = A \cos(\omega t - kx)$.Given equation: $y = 5 \cos(200\pi t - \frac{\pi x}{150})$.Comparing the given equation with the standard form, we identify the angular frequency $\omega = 200\pi 	ext{ rad/s}$ and the wave number $k = \frac{\pi}{150} 	ext{ rad/cm}$.The wave velocity $v$ is given by the formula $v = \frac{\omega}{k}$.Substituting the values: $v = \frac{200\pi}{\pi/150} = 200 	imes 150 = 30000 	ext{ cm/s}$.To convert the velocity into m/s,we divide by $100$: $v = \frac{30000}{100} = 300 	ext{ m/s}$.

The equation of a plane progressive wave is given by $y = 5 \cos \pi (200t - \frac{x}{150})$ where $x$ and $y$ are in cm and $t$ is in second. The velocity of the wave is . . . . . . m/s.

Similar Questions

Among the following,the equation representing a progressive wave is
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$(D)$ $y=\cos x \sin t+\cos 2x \sin 2t$

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