The diagram shows an instantaneous position of a string as a transverse progressive wave travels along it…

The diagram shows an instantaneous position of a string as a transverse progressive wave travels along it from left to right. Which one of the following correctly shows the direction of velocity of points 1, 2 and 3 on the string? A diagram showing instantaneous position of a wave on a string with points 1, 2, and 3 marked on it.
  1. 1: $\uparrow$, 2: $\downarrow$, 3: $\downarrow$
  2. 1: $\uparrow$, 2: $\downarrow$, 3: $\uparrow$
  3. 1: $\downarrow$, 2: $\downarrow$, 3: $\downarrow$
  4. 1: $\downarrow$, 2: $\uparrow$, 3: $\downarrow$

Solution

Particle velocity $(v_p) = -v \times \text{Slope of the graph at that point.}$ At point 1 Slope of the curve is positive, hence particle velocity is negative or downward ($\downarrow$). At point 2 Slope is negative, hence particle velocity is positive or upwards ($\uparrow$). At point 3 Again, slope of the curve is positive, hence particle velocity is negative or downward ($\downarrow$).

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