Transverse Wave in a String Reflection and Transmission

In summary, the conversation discusses the determination of reflected and transmitted waves in a system consisting of a string with density/length of rho and tension T, and an elastic spring with stiffness k at x=0. The system is subjected to a step pulse (fi = H(t)) at the location of the spring. The boundary conditions for this system are presented as y(0-,t) = y(0+,t) ----> fi(-ct) + gr(ct) = ft(-ct) and Ty' = ky at x = 0. The conversation concludes with a query about the appropriate boundary condition to use and the next steps in the analysis.
  • #1
artongue
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A string with a density/length of rho and tension T has an elastic spring with stiffness k at x=0. There is a step pulse (fi = H(t)) incident on this discontinuity. Determine the reflected and transmitted waves.

Im not sure what boundary condition to use at the location of the spring. All I have now is:

BCs: (y(x,t) is deflection, fi(x-ct) is incident wave, gr(x+ct) is reflected, ft(x-ct) is transmitted)

y(0-,t) = y(0+,t) ----> fi(-ct) + gr(ct) = ft(-ct)

Not sure what other BC to use. Maybe Ty' = ky at x = 0? Where do I go from there?
 
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  • #2
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FAQ: Transverse Wave in a String Reflection and Transmission

1. What is a transverse wave in a string?

A transverse wave in a string is a type of mechanical wave that travels along a string or rope and causes the particles of the string to move up and down perpendicular to the direction of the wave. This type of wave is commonly seen in musical instruments such as guitars and violins.

2. How does reflection occur in a transverse wave in a string?

Reflection occurs in a transverse wave in a string when the wave encounters a boundary, such as the end of the string or a fixed point, and is then sent back in the opposite direction. This can result in interference patterns and standing waves.

3. What is the difference between transmission and reflection in a transverse wave in a string?

Transmission refers to the continuation of a wave through a boundary, while reflection refers to the bouncing back of the wave off of a boundary. In the case of a transverse wave in a string, transmission would occur when the wave continues along the string, while reflection would occur when the wave is sent back in the opposite direction.

4. How does the tension in a string affect the reflection and transmission of a transverse wave?

The tension in a string affects the speed at which a transverse wave travels along the string. This, in turn, affects the wavelength and frequency of the wave. A higher tension can result in a faster wave speed, shorter wavelength, and higher frequency. This can also affect the amount of reflection and transmission that occurs.

5. Can a transverse wave in a string be both reflected and transmitted at the same time?

Yes, a transverse wave in a string can be both reflected and transmitted at the same time. This is often seen in situations where the wave encounters multiple boundaries, resulting in both reflection and transmission at each boundary. This can create complex interference patterns and standing waves.

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