Question

A wire is stretched between two posts. Another wire is stretched between two posts that are four times as far apart. The tension in the wires is the same, and they have the same mass. A transverse wave travels on the shorter wire with a speed of 190 m/s. What would be the speed of the wave on the longer wire?

Answer 1

Answer:

Therefore,

The speed of the wave on the longer wire is 95 m/s.

Explanation:

Given:

For Short wire, speed is

$v_{s}=190\ m/s$

Let length of Short  and Longer wire be $L_{s}\ and\ L_{l}$ such that

$L_{l}=4\times L_{s}$

To Find:

$v_{l}=?$  Speed on the longer wire

Solution:

The speed of a pulse or wave on a string under tension can be found with the equation,

$v=\sqrt{\dfrac{F_{T}\times L}{m}$

Where,

$F_{T}$ = Tension on the wire

L = Length of Sting

m = mass of String

So here we have,

$F_{T}$ = same

$L_{l}=4\times L_{s}$

Therefore,

$v_{s}=\sqrt{\dfrac{F_{T}\times L_{s}}{m}$ ......equation ( 1 )

And

$v_{l}=\sqrt{\dfrac{F_{T}\times L_{l}}{m}$  .......equation ( 2 )

Dividing equation 1 by equation 2 and on Solving we get

$\dfrac{v_{s}}{v_{l}}=\sqrt{\dfrac{L_{s}}{L_{l}}}$

Therefore,

$v_{l}=v_{s}\sqrt{\dfrac{4\times L_{s}}{L_{s}}}=190\times 2=380\ m/s$

Therefore,

The speed of the wave on the longer wire is 95 m/s.