Question

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. 1 2 3
  $\uparrow$ $\downarrow$ $\downarrow$
• B. 1 2 3
  $\uparrow$ $\downarrow$ $\uparrow$
• C. 1 2 3
  $\downarrow$ $\downarrow$ $\downarrow$
• D. 1 2 3
  $\downarrow$ $\uparrow$ $\downarrow$

Answer 1

The correct option is D 1 2 3

$\downarrow$ $\uparrow$ $\downarrow$
The direction of velocity of a particle in a progressive wave is given by,

$v_p=-v\times m$

where,
$v_p\to$ particle velocity.
$v\to$ velocity of progressive wave ,
$m\to$ slope of the point on the wave.

At point $1:$ Slope of the curve is positive, hence particle velocity is negative or downwards $(\downarrow )$

At point $2:$ Slope of the curve 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 $(\downarrow )$

Hence, option (d) is the correct answer.