Answer:
The new velocity of the string is 100 centimeters per second (1 meter per second).
Explanation:
The speed of a wave through a string ([tex]v[/tex]), in meters per second, is defined by the following formula:
[tex]v = \sqrt{\frac{T\cdot L}{m} }[/tex] (1)
Where:
[tex]T[/tex] - Tension, in newtons.
[tex]L[/tex] - Length of the string, in meters.
[tex]m[/tex] - Mass of the string, in kilograms.
The expression for initial and final speeds of the wave are:
Initial speed
[tex]v_{o} = \sqrt{\frac{T_{o}\cdot L_{o}}{m_{o}} }[/tex] (2)
Final speed
[tex]v = \sqrt{\frac{(4\cdot T_{o})\cdot (0.5\cdot L_{o})}{2\cdot m_{o}} }[/tex]
[tex]v = \sqrt{\frac{T_{o}\cdot L_{o}}{m_{o}} }[/tex] (3)
By (2), we conclude that:
[tex]v =v_{o}[/tex]
If we know that [tex]v_{o} = 1\,\frac{m}{s}[/tex], then the new speed of the wave in the string is [tex]v = 1\,\frac{m}{s}[/tex].
