Answer:
Therefore,
The speed of the wave on the longer wire is 95 m/s.
Explanation:
Given:
For Short wire, speed is
[tex]v_{s}=190\ m/s[/tex]
Let length of Short and Longer wire be [tex]L_{s}\ and\ L_{l}[/tex] such that
[tex]L_{l}=4\times L_{s}[/tex]
To Find:
[tex]v_{l}=?[/tex] Speed on the longer wire
Solution:
The speed of a pulse or wave on a string under tension can be found with the equation,
[tex]v=\sqrt{\dfrac{F_{T}\times L}{m}[/tex]
Where,
[tex]F_{T}[/tex] = Tension on the wire
L = Length of Sting
m = mass of String
So here we have,
[tex]F_{T}[/tex] = same
[tex]L_{l}=4\times L_{s}[/tex]
Therefore,
[tex]v_{s}=\sqrt{\dfrac{F_{T}\times L_{s}}{m}[/tex] ......equation ( 1 )
And
[tex]v_{l}=\sqrt{\dfrac{F_{T}\times L_{l}}{m}[/tex] .......equation ( 2 )
Dividing equation 1 by equation 2 and on Solving we get
[tex]\dfrac{v_{s}}{v_{l}}=\sqrt{\dfrac{L_{s}}{L_{l}}}[/tex]
Therefore,
[tex]v_{l}=v_{s}\sqrt{\dfrac{4\times L_{s}}{L_{s}}}=190\times 2=380\ m/s[/tex]
Therefore,
The speed of the wave on the longer wire is 95 m/s.
