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(B) progressive wave is represented by a function of the form $y = f(ax \pm bt)$. Option $(A)$ represents a standing wave because it is a product of s

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$C$

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(B) progressive wave is represented by a function of the form $y = f(ax \pm bt)$. Option $(A)$ represents a standing wave because it is a product of spatial and temporal functions. Option $(B)$ is not a periodic function. Option $(C)$ can be rewritten using the identity $A \sin 	heta + B \cos 	heta = R \sin(	heta + \phi)$,where $R = \sqrt{3^2 + 4^2} = 5$. Thus,$y = 5 \sin(5x - 0.5t + \phi)$,which is a standard progressive wave equation. Option $(D)$ is a superposition of two different waves with different frequencies and wave numbers,not a single progressive wave. Therefore,only $(C)$ represents a single progressive wave.

Among the following,the equation representing a progressive wave is
$(A)$ $y=2 \cos 3x \sin 10t$
$(B)$ $y=2 \sqrt{x-vt}$
$(C)$ $y=3 \sin (5x-0.5t)+4 \cos (5x-0.5t)$
$(D)$ $y=\cos x \sin t+\cos 2x \sin 2t$

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Among the following,the equation representing a progressive wave is$(A)$ $y=2 \cos 3x \sin 10t$$(B)$ $y=2 \sqrt{x-vt}$$(C)$ $y=3 \sin (5x-0.5t)+4 \cos (5x-0.5t)$$(D)$ $y=\cos x \sin t+\cos 2x \sin 2t$