Arbitrary travelling wave on string (griffiths 9.5)

The reflected wave will be identical to the incoming wave, but with a different amplitude and phase. The transmitted wave, on the other hand, will have a different shape and amplitude, depending on the mass densities of the two strings. In summary, the conversation discusses the problem of a traveling wave on a string with two different mass densities and how to determine the transmitted and reflected waves. The solution involves imposing continuity conditions and does not require decomposing the wave using Fourier series. The reflected wave will be identical to the incoming wave, while the transmitted wave will have a different shape and amplitude.
  • #1
DE7
8
0
hi all,

i'm in need of a little help with griffiths 9.5 (EM). the problem concerns a traveling wave of arbitrary shape on a string. the string consists of two strings with different mass densities tied together at z=0. given the arbitrary incoming wave, what are the transmitted and reflected waves?

i know i must impose continuity conditions on the wave and its derivatives at z=0. however, are these two equations enough to determine the problem? or should i decompose the incoming wave using Fourier series? I'm not too sure how to go about doing that...any hints?
 
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  • #2
The problem of wave reflection and transmission is derived simply from the principle of continuity, so yes they are enough. Whether you decompose the wave or not into its fundamental harmonics is irrelevant to the reflected and transmitted wave magnitudes, which is usually the parameter of interest.

Reflection occurs when there is a change in propagating medium, such as air to glass, or string1 to string 2 for mechanical waves.
 

1. What is an arbitrary travelling wave on a string?

An arbitrary travelling wave on a string refers to a wave that can have any shape or form and is moving along a string or rope. This type of wave can be described using a mathematical formula, taking into account the properties of the string such as tension, density, and length.

2. How is an arbitrary travelling wave different from a regular wave?

An arbitrary travelling wave is different from a regular wave in that it does not have a specific frequency or wavelength. It can also have varying amplitudes at different points along the string, unlike a regular wave which has a constant amplitude.

3. What is the significance of studying arbitrary travelling waves on a string?

Studying arbitrary travelling waves on a string allows scientists to understand the behavior of waves in different physical systems. It also helps in developing mathematical models that can be applied to other types of waves, such as electromagnetic waves or sound waves.

4. How is arbitrary travelling wave on a string related to the wave equation?

The wave equation is a partial differential equation that describes the behavior of waves. By studying arbitrary travelling waves on a string, scientists can derive and understand the wave equation in a more tangible and physical way.

5. What are some real-world applications of arbitrary travelling waves on a string?

Arbitrary travelling waves on a string have various real-world applications, such as in musical instruments, earthquake detection and prediction, and studying the properties of materials. They also have implications in fields like acoustics, optics, and electronics.

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