Two strings connected by a spring

In summary: Lesson-3/Boundary-BehaviorScroll down about 1/2 way forTransmission of a Pulse Across a Boundary from Less to More Densetho the whole page may be enlightening to youTransmission of a Pulse Across a Boundary from Less to More DenseThere are many uses for waves, one of which is understanding how they propagate through boundaries. In this lesson, we will look at how a pulse propagates across a boundary from less dense to more dense media.
  • #1
Karthiksrao
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55 Hi all,

Hello,

Racking my brains over this :

If I have two semi-infinite strings (made of same material) - which are connected by a massless spring, and now I send a longitudinal wave along one string.

Will the spring just pass on the wave to the other string or will it serve to reflect some of it back ?

If it does reflect some of it back, what would be the boundary conditions that you will have to impose ?

Is it just that the E * du/dx which is the stress in the two strings, should be equal to k*(u1 - u2) where u1 and u2 are the displacements of the two strings at the interface between the string and the spring ? So I will just have:

E * du1 /dx = -k * (u1 - u2)
E * du2 /dx = k * (u1 - u2)

One of the right hand sides is of opposite sign as the direction of force is opposite.

Not able to show energy conservation with this. Perhaps I am using the wrong boundary conditions ?

Thanks!

Thanks!
 
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  • #2
Karthiksrao said:
Will the spring just pass on the wave to the other string or will it serve to reflect some of it back ?

what do you think and why ?Dave
 
  • #3
When the spring compresses as the wave reaches it, it exerts a force back at the thread. This would cause some of the momentum of the wave to change direction. So it should be reflected partly...?
 
  • #4
Karthiksrao said:
end a longitudinal wave along one string
Waves in strings are usually transverse. How do you effectively couple a longitudinal wave onto a string? Do you have a physical system in mind with this question?
 
  • #5
Maybe something like the can (or paper cup) "telephone". :)
 
  • #6
nasu said:
Maybe something like the can (or paper cup) "telephone". :)
Ah, good point!

@Karthiksrao -- Are you familiar with the Wave Equation and how it's derived? Also, how long is the weightless spring compared to the wavelength of your longitudinal wavelength? What is the relationship between the spring constant k and the equivalent parameter for the string?
 
  • #7
Yes indeed I am more than familiar with the wave equation and its derivation. The wavelength and length of the spring is of the same order - so the wave sees the spring. Likewise, the spring constant and the material elastic constant are enough to affect each other.

My point is not to solve a problem with given parameters. That is immaterial.

What I am trying to figure out is how we can go about approaching this problem, Intuitively I do feel there will be reflection and transmission, but what would be the boundary conditions for a wave at the 'spring interface'

Many thanks
 
  • #8
Karthiksrao said:
What I am trying to figure out is how we can go about approaching this problem, Intuitively I do feel there will be reflection and transmission, but what would be the boundary conditions for a wave at the 'spring interface'

have a look at this site
http://www.physicsclassroom.com/class/waves/Lesson-3/Boundary-Behavior

scroll down about 1/2 way for
Transmission of a Pulse Across a Boundary from Less to More Dense

tho the whole page may be enlightening to youOverall, your query is also the basis of impedance mismatches in transmission lines at termination points etc and the losses incurred, standing waves generated etc :smile:
amongst many other uses ...
In my seismology studies when doing seismic reflection of sound waves transmitted into the earth
to determine densities of the different rock layers etc

you might also be interested in this classic old Bell Labs teaching video
on wave propagation, reflection etc


cheers
Dave
 
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Related to Two strings connected by a spring

What is the concept of two strings connected by a spring?

The concept of two strings connected by a spring is a physical system in which two strings are attached to each end of a spring. The spring acts as a connector between the two strings, allowing for movement and energy transfer between them.

How does the spring affect the movement of the strings?

The spring affects the movement of the strings by applying a restoring force that opposes any displacement of the strings from their equilibrium position. This causes the strings to oscillate back and forth around their resting point.

What factors influence the behavior of the strings connected by a spring?

The behavior of the strings connected by a spring is influenced by several factors, including the stiffness of the spring, the mass of the strings, and the amplitude of the oscillations. These factors affect the frequency, period, and amplitude of the oscillations.

How is the energy transferred between the strings in this system?

The energy is transferred between the strings in this system through the spring. As the strings move, they stretch and compress the spring, storing potential energy. This energy is then released as the spring pushes back, causing the strings to move in the opposite direction.

What are some real-life applications of two strings connected by a spring?

Two strings connected by a spring have various real-life applications, such as in musical instruments like guitars and violins, where the strings are attached to a bridge that is connected to the instrument's body by a spring. They are also used in engineering to absorb shock and vibrations in buildings and bridges, and in suspension systems of vehicles to provide a smoother ride.

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