Answer:
On the standing waves on a string, the first antinode is one-fourth of a wavelength away from the end. This means
This means that the relation between the wavelength and the length of the string is
By definition, this standing wave is at the third harmonic, n = 3.
Furthermore, the standing wave equation is as follows:
The bead is placed on x = 0.138 m. The maximum velocity is where the derivative of the velocity function equals to zero.
For this equation to be equal to zero, sin(59.94t) = 0. So,
This is the time when the velocity is maximum. So, the maximum velocity can be found by plugging this time into the velocity function: