When and where do two transverse waves on strings overtake each other?

[palkia]

Homework Statement

Two long strings P and Q ,each having linear mass density 1.2 x 10^-2
are stretched by a different tension 4.8 N and 7.5 N respectively and are kept parallel to each other with their left ends at x=0.Wave pulses are produced on the strings at t=0 on string P and at t=20ms at string Q.When and where will the pulses on Q overtake at on P.

Homework Equations

The Attempt at a Solution

Using the wave equation for the string ,I found the velocity at x=0 for P and Q to be 20m/s and 25m/s respectively.But I have one doubt about this question.Shouldn't speed of a wave in a string change with respective positions due to change in tension throughout the string...So does this not contradict the question

 

[Orodruin]

What change in tension?

 

[palkia]

Change in tension in a rope having masses incrases linearly throughout the rope

 

[Orodruin]

You are thinking of a freely hanging rope. There is nothing in the problem formulation indicating that this is the case.

Also, you should always state units when giving values.

 

[palkia]

What is the difference between freely hanging rope and this case?

I will keep in mind to mention the units next time .

 

[Orodruin]

A hanging rope has a gravitational force acting on it in its longitudinal direction. For force equilibrium, this means tension has to vary accordingly.

 

[palkia]

And what does this case look like...are we holding the rope?

 

[Orodruin]

The strings are kept taut by pulling them at each end.

 

[palkia]

Okay.I got this then

Thanx