When a transverse sinusoidal wave propagates to the right along a string,
the displacement of an element of the string located at position x can be
Transverse velocity of an element of a string
This element moves in a direction which is transverse to the motion of the
wave. The velocity associated with this transverse motion is the rate
at which the element is moving up and down and it is called the transverse
velocity of the element. To distinguish it from the velocity of the wave, we
use u as the symbol for the transverse velocity.
The transverse velocity u of an element changes in a sinusoidal
manner as a function of time and position while the velocity of the wave v
is a constant quantity.
The transverse speed is maximum when the displacement of the element is zero
and the transverse speed is zero when the displacement is maximum or