A transverse
harmonic wave traveling on a string is described by

where x and y are in meters and t is in seconds.

- What is the speed of the wave?
- Find an expression for the transverse velocity of an element of the string located at position x and at time t.
- What is the maximum transverse speed? Where does it occur?
- Find an expression for the transverse acceleration of an element of the string located at position x and at time t.
- What is the maximum transverse acceleration? Where does it occur?

Example 3

a. The speed of the wave is

Answer

b. The transverse velocity is

c. The maximum transverse
velocity is

It occurs when the displacement of an element of the string becomes zero.

d. The transverse acceleration is

e. The maximum transverse acceleration is

It occurs when the displacement of an element of the string becomes maximum,
y = y_{m}, or minimum, y = -y_{m} .