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(D) The particle velocity $v_p$ is given by $v_p = -v \cdot (	ext{slope})$, where $v$ is the wave speed and slope is $\frac{\partial y}{\partial x}$.

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both $(B)$ and $(C)$

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(D) The particle velocity $v_p$ is given by $v_p = -v \cdot (	ext{slope})$, where $v$ is the wave speed and slope is $\frac{\partial y}{\partial x}$.$1$. For point $P$: The slope is positive. Since the wave is moving to the right, $v_P = -v \cdot (	ext{positive slope}) $2$. For points $Q$ and $R$: Both points are at the same distance from the origin on opposite sides of the $y$-axis. By symmetry, the slopes at $Q$ and $R$ have equal magnitudes and are both negative. Since $v_Q = -v \cdot (	ext{slope}_Q)$ and $v_R = -v \cdot (	ext{slope}_R)$, and $	ext{slope}_Q = 	ext{slope}_R $3$. Comparing magnitudes: The slope at $P$ is steeper than the slopes at $Q$ and $R$. Therefore, $|v_P| > |v_Q| = |v_R|$.Thus, both statements $(B)$ and $(C)$ are correct.

Column-$1$	Column-$2$
$(a)$ Light waves	$(i)$ Mechanical and transverse.
$(b)$ Sound waves	$(ii)$ Mechanical and longitudinal.
$(c)$ Earthquake waves	$(iii)$ Non-mechanical and transverse.
$(d)$ Waves on a tense string	$(iv)$ Mechanical,transverse and longitudinal.

At a certain moment, the photograph of a string on which a harmonic wave is travelling to the right is shown. Then, which of the following is true regarding the velocities of the points $P$, $Q$ and $R$ on the string?

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