How Long Does It Take for a Transverse Wave to Travel Through a Whirling Rope?

In summary, the wave travels from the top to the bottom of the rope in a circular path. The tension in the string is equal to the radius of the circular path.
  • #1
kidsmoker
88
0

Homework Statement



"A uniform rope with length L and mass m is held at one end and whirled in a horizontal circle with angular velocity w. You can ignore the force of gravity on the rope. Find the time required for a transerve wave to travel from one end of the rope to the other."


Homework Equations



w = 2*pi*f
wave speed = frequency*wavelength = sqrt(tension/mass per unit length)

The Attempt at a Solution



I'm a bit confused here. If the force of gravity on the rope is being ignored, then what is the tension in the rope?
 
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  • #2
Hi kidsmoker,

kidsmoker said:

Homework Statement



"A uniform rope with length L and mass m is held at one end and whirled in a horizontal circle with angular velocity w. You can ignore the force of gravity on the rope. Find the time required for a transerve wave to travel from one end of the rope to the other."


Homework Equations



w = 2*pi*f
wave speed = frequency*wavelength = sqrt(tension/mass per unit length)

The Attempt at a Solution



I'm a bit confused here. If the force of gravity on the rope is being ignored, then what is the tension in the rope?

Think about what has to be true for the mass to travel in a circular path.
 
  • #3
There's a force mw^2A acting towards the centre? Do I take this as the tension in the string? I'm still not sure what to do sorry...
 
Last edited:
  • #4
kidsmoker said:
There's a force mw^2A acting towards the centre? Do I take this as the tension in the string? I'm still not sure what to do sorry...

What is "A" in your equation?
 
  • #5
Sorry, the radius of the circular motion. I called it A cos it's like the amplitude.
 
  • #6
kidsmoker said:
Sorry, the radius of the circular motion. I called it A cos it's like the amplitude.

In your problem that is actually "L" and yes that is the centripetal force on the string which is your Tension that you are looking for.
 
  • #7
Are you sure? Why would it be equal to the length of the string?
 
  • #8
kidsmoker said:
Are you sure? Why would it be equal to the length of the string?

Perhaps this will help?
http://hyperphysics.phy-astr.gsu.edu/hbase/cf.html#cf
Wait a minute is there a mass at the end of the rope or is the rope itself mass M total?

Maybe I am misreading the problem?
 
Last edited:
  • #9
I ws completely misreading the question too. I thought that the string was hanging vertically and you were whirling the top end in a circle, so that these circular waves travel down the string. I realize now that it means that the whole string is horizontal and it's being whirled in a circle like this, so as to keep it taut. In that case the problem is easy :P

Thanks anyway!
 

Related to How Long Does It Take for a Transverse Wave to Travel Through a Whirling Rope?

1. What is a wave in a string?

A wave in a string is a disturbance that travels through a medium, such as a string, by transferring energy from one particle to the next. It can be described by its wavelength, amplitude, and frequency.

2. How is a wave in a string created?

A wave in a string is created by an initial disturbance or energy source, such as plucking a guitar string. This disturbance causes the particles in the string to vibrate and transfer energy to neighboring particles, creating a wave that travels along the string.

3. What factors affect the speed of a wave in a string?

The speed of a wave in a string is affected by the tension and density of the string, as well as the wavelength and frequency of the wave. Higher tension and lower density will result in a faster wave speed, while longer wavelengths and lower frequencies will result in a slower wave speed.

4. How does a wave in a string differ from a sound wave?

A wave in a string is a mechanical wave that travels through a medium, while a sound wave is a pressure wave that can travel through both a medium and a vacuum. The speed of a wave in a string is also dependent on the properties of the string, while the speed of a sound wave is dependent on the properties of the medium it is traveling through.

5. What are some real-world applications of a wave in a string?

A wave in a string has many practical applications, such as musical instruments like guitars and violins, communication systems using fiber optics, and seismic exploration for oil and gas. It is also used in scientific experiments to study the properties of waves and their behavior.

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