A string of length 8 m, which has a total mass of 5 g, is stretched along the x-axis and put under a tension of 9 N. One end of the string is attached to a simple harmonic oscillator that is fixed in place at x = 0 but free to move in the ±y direction. The maximum displacement of the oscillator is 3 cm above or below the x-axis, and it completes 60 cycles every second. At time t = 0, the oscillator is at y = −3 cm. (a) Write the wave function ?(?,?) for the vertical displacement of particles along the string.
A string of length 8 m, which has a total mass of 5 g, is stretched along
the x-axis and put under a tension of 9 N. One end of the string is attached to a simple
harmonic oscillator that is fixed in place at x = 0 but free to move in the ±y direction.
The maximum displacement of the oscillator is 3 cm above or below the x-axis, and it
completes 60 cycles every second. At time t = 0, the oscillator is at y = −3 cm.
(a) Write the wave function ?(?,?) for the vertical displacement of particles along the
string.
(b) Obtain an expression for the mechanical energy per unit length of the string, dEtot/dx, as a function of x and t. Integrate this along the length of the string to find its total
energy content, at a fixed time ?0.
Step by step
Solved in 2 steps
