Unraveling the Physics of Strings: Tension, Velocity & Slope

[reza1]

Just a couple of Questions:
for the wave function y(x,t) = A / (x-vt)^2+b ------> What is the importance of 'b' and what is its meaning?

A Uniform Circular Hoop of string of mass m and radius r is rotating in the absence of gravity. Its tangential speed is Vo. Its length is deltax=r*delta(pheta)

Find the Tension in the Spring
Linear Density= u
Length = x
Mass = u * delta x
ac=centripetal acceleration
(u*deltax)ac=2Ft + sin1/2(pheta)
(u*r*delta(pheta))Vo^2/r=2Ft1/2(pheta) ---> Assuming small angle for Sin
uVo^2= Ft

Find the speed of a wave traveling on the string
Do i have to find the 2nd derivative of ASin(kx-wt) for the velocity?Another Question
Two strings of Linear Density u1 and u2 are tied together at x=0 and stretched along the x-axis with a tension F. A wave given by y(x,t)=Asink1(x-v1t) travels in the string of linear density u1. When it meets the knot it is both reflected, giving a wave Csink1(x+v1t) and transmitted giving a wave Bsink2(x-V2t)

What is the Physical Interpretation of the assumption that k1v1=k2v2
Just need some help to start this question

What is the Physical interpretation of the assumption that the strings have the same slope at the knot

if the length and frequency of the knot is held constant and the tension varies, both strings will have the same slope ? ---> I am not to sure about this Help on any of these questions will be much appreciated thank yiou

 

[Shooting Star]

A Uniform Circular Hoop of string of mass m and radius r is rotating in the absence of gravity. Its tangential speed is Vo. Its length is deltax=r*delta(pheta)

Find the Tension in the Spring

What do you mean by saying that the length of the string is Δx? The derivation you have given is correct, but I'm not sure you have understood the derivation correctly.

Find the speed of a wave traveling on the string
Do i have to find the 2nd derivative of ASin(kx-wt) for the velocity?

Use the same formula for the speed of transverse wave in a taut string.

Two strings of Linear Density u1 and u2 are tied together at x=0 and stretched along the x-axis with a tension F. A wave given by y(x,t)=Asink1(x-v1t) travels in the string of linear density u1. When it meets the knot it is both reflected, giving a wave Csink1(x+v1t) and transmitted giving a wave Bsink2(x-V2t)

What is the Physical Interpretation of the assumption that k1v1=k2v2

What does kv represent in wave motion?

What is the Physical interpretation of the assumption that the strings have the same slope at the knot

The transverse component of the tension, which is -T\frac{\partial}{\partial x} y(x,t) should be continuous across the boundary; otherwise it'll give rise to infinite forces.