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A Complete Resource Book in Physics for JEE Main
Two wave pulses are generated in a string. One of the pulses is given by equation $y_{1}=A \sin (\omega t-k x)$. If average power transmitted by both the pulses along the string are same and is given by $P=\frac{T A^{2} \omega^{2}}{2 v}$, where $T$ is the tension in the string, $A$ is amplitude of a pulse, $\omega$ is angular frequency of the source, and $v$ is wave velocity, then which one of the following equations may represent the other wave pulse?
(A) $y_{2}=\frac{A}{\sqrt{2}} \sin (2 \omega t-k x)$
(B) $y_{2}=\frac{A}{\sqrt{2}} \sin (\omega t-2 k x)$
(C) $y_{2}=2 A \sin \left(\frac{\omega t}{2}-k x\right)$
(D) $y_{2}=2 A \sin \left(\frac{\omega t}{2}-\frac{k x}{2}\right)$