Unraveling the Physics of Strings: Tension, Velocity & Slope

In summary, the experts discuss various questions related to wave functions, tension in a spring, speed of a wave, physical interpretation of assumptions, and the relation between linear density and wave motion. They also clarify the concept of string length and provide a formula for calculating wave speed in a taut string. They also mention the importance of having continuous transverse tension for avoiding infinite forces.
  • #1
reza1
3
0
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
 
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  • #2
reza1 said:
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[itex]\frac{\partial}{\partial x}[/itex] y(x,t) should be continuous across the boundary; otherwise it'll give rise to infinite forces.
 
Last edited:

What is the concept of tension in strings?

Tension is a force that is applied to a string in order to stretch it. It is the force that pulls the string taut and keeps it in place. In the context of physics, tension is often represented by the symbol T and has units of newtons (N).

How does tension affect the velocity of a string?

The tension in a string is directly proportional to its velocity. This means that as the tension increases, the velocity of the string also increases. This relationship is described by the wave equation, which states that the velocity of a wave is equal to the square root of the tension divided by the linear density of the string.

What is the significance of the slope in the physics of strings?

The slope of a string, also known as its gradient, is an important factor in understanding the behavior of strings. It represents the change in tension per unit length of the string. A steeper slope indicates a greater change in tension and therefore a higher velocity of the string.

How does the tension and slope of a string affect its frequency?

The tension and slope of a string are both directly related to the frequency of the string. As the tension increases, the frequency of the string also increases. Similarly, a steeper slope results in a higher frequency. This is because both tension and slope affect the speed at which waves travel through the string, which in turn determines the frequency.

What are some real-life applications of understanding the physics of strings?

The physics of strings has numerous practical applications, such as in musical instruments, engineering design, and medical imaging. Understanding the relationship between tension, velocity, and slope allows for the design and optimization of string-based systems, such as guitar strings and suspension bridges. Additionally, techniques such as string resonance are used in medical imaging to create detailed images of internal structures.

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