- #1

- 296

- 0

Please look at this

http://jpkc.fudan.edu.cn/picture/ar...e965/0b6e686f-6716-4d52-ba65-79ae2a87d8fa.ppt

Energy in Travelling Wave

[The same information is in Resnick Haliday & Krane,so its not wrong.Whatever am typing is from an authentic source]

Now I have a doubt.

Why dint they use the net force which is F*d2y/dx2 ...ie Td(tan q) where q is the angle made by the force with the horizontal.

If we see a particle then its left particle is pulling it with a force F and its right particle is also pulling it with a force F.These forces are just a little tilted so they dont cancel out.

We see that for a travelling wave dU/dt =dK/dT ie change in potential energy is equal to change in Kinetic energy.(Not -ve of it which is reasonable as energy is being transmitted.)

We find that at the peak the KE and PE is 0(or minimum) and at its equilibrium position its maximum.

The reason they give for PE being maximum at the equilibrium position is that the string is stretched maximum at that position.(as dy/dx is maximum then).So PE is maximum

However if we look at it for a standing wave the PE is maximum at the peak and minimum at the equilibrium position.

Now how do we derive that

{this is what I used-dint find it,so this can be wrong}

If we use the standing wave equation y=2Asin(kx)cos(wt)

& use dK=1/2*u*dx*(dy/dt)^2 {u being linear mass density so this is (1/2)*m*v^2)

and dU as 1/2*F*(dy/dx)^2 {which is the formula used in the link and Resnick Halliday)

we find dU as 2*u*w^2*dx*(a)^2*cos^2(kx)*cos^(wt) {cos^2 (kx) is cos(kx) whole square }

and dK as 2*u*w^2*dx*a^2*sin^2(kx)*sin^(wt)

which shows that for a standing wave the PE is 0 at peak as cos^2(kx) is 0

However Sources all over the net say that for a standing wave the PE is maximum at peak.

Also this equation shows that dU/dt is not equalt to -dK/dt

Also why is this difference in standing and travelling waves coming into play ?

Please try to help guys.

Thanks

http://jpkc.fudan.edu.cn/picture/ar...e965/0b6e686f-6716-4d52-ba65-79ae2a87d8fa.ppt

Energy in Travelling Wave

[The same information is in Resnick Haliday & Krane,so its not wrong.Whatever am typing is from an authentic source]

Now I have a doubt.

**Question 1****When they derived the equation for potential energy they used the tension force acting on the particle by the particle to the left of it?**Why dint they use the net force which is F*d2y/dx2 ...ie Td(tan q) where q is the angle made by the force with the horizontal.

If we see a particle then its left particle is pulling it with a force F and its right particle is also pulling it with a force F.These forces are just a little tilted so they dont cancel out.

**Question 2**We see that for a travelling wave dU/dt =dK/dT ie change in potential energy is equal to change in Kinetic energy.(Not -ve of it which is reasonable as energy is being transmitted.)

We find that at the peak the KE and PE is 0(or minimum) and at its equilibrium position its maximum.

The reason they give for PE being maximum at the equilibrium position is that the string is stretched maximum at that position.(as dy/dx is maximum then).So PE is maximum

However if we look at it for a standing wave the PE is maximum at the peak and minimum at the equilibrium position.

Now how do we derive that

{this is what I used-dint find it,so this can be wrong}

If we use the standing wave equation y=2Asin(kx)cos(wt)

& use dK=1/2*u*dx*(dy/dt)^2 {u being linear mass density so this is (1/2)*m*v^2)

and dU as 1/2*F*(dy/dx)^2 {which is the formula used in the link and Resnick Halliday)

we find dU as 2*u*w^2*dx*(a)^2*cos^2(kx)*cos^(wt) {cos^2 (kx) is cos(kx) whole square }

and dK as 2*u*w^2*dx*a^2*sin^2(kx)*sin^(wt)

which shows that for a standing wave the PE is 0 at peak as cos^2(kx) is 0

However Sources all over the net say that for a standing wave the PE is maximum at peak.

Also this equation shows that dU/dt is not equalt to -dK/dt

**Question 3**

So how do we actually prove mathematically that PE is maximum at the Peak and minimum at equilibrium positions.So how do we actually prove mathematically that PE is maximum at the Peak and minimum at equilibrium positions.

Also why is this difference in standing and travelling waves coming into play ?

Please try to help guys.

Thanks

Last edited: