Given:
If the tension force on the rope is double the speed of the wave on the rope will doubled as well.
Required: To determine whether the given statement is true or false
Explanation:
The relation between tension force and speed is
[tex]\begin{gathered} speed\propto\sqrt{tension\text{ force}} \\ v\propto\sqrt{T} \end{gathered}[/tex]On doubling the tension force, the speed will be
[tex]\begin{gathered} v^{\prime}\propto\sqrt{2T} \\ \propto\sqrt{2}\times T \end{gathered}[/tex]Thus, the speed of the wave will be square root times the tension.
Final Answer: The given statement is false
