1-5 Speed of a sinusoidal traveling wave
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 = ym, or minimum, y = -ym .
