Sinusoidal wave traveling along a composite string

The wave number changes depending on the mass/length density of the string sections.In summary, the conversation discusses a scenario of a sinusoidal wave traveling along a string composed of two sections with different mass/length density, and the question of whether the transmitted and reflected waves will have the same wave number or frequency. It is mentioned that the whole string is under tension, and the answer is that the frequency remains the same while the wave number changes based on the mass/length density of the string sections.
  • #1
golnat
6
0
I've been working on this one for quite some time...

Consider a sinusoidal wave traveling along a string composed of two sections, one with a lighter mass/length density than the other. A pulse is traveling in the light region and about to hit the junction. If the incident wave is given by y_i(x,t)=A_i*sin(wt-k1x), will the transmitted and reflected waves have the same wave number or frequency?
 
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  • #2
forgot to mention the fact that the whole string is under tension F
 
  • #3
golnat said:
will the transmitted and reflected waves have the same wave number or frequency?
The frequency remains the same.
 

1. How does a sinusoidal wave travel along a composite string?

A sinusoidal wave travels along a composite string by causing the particles of the string to vibrate in a back-and-forth motion, creating a wave-like pattern. This wave travels along the string at a constant speed, determined by the tension and mass of the string.

2. What factors affect the speed of a sinusoidal wave traveling along a composite string?

The speed of a sinusoidal wave traveling along a composite string is affected by the tension and mass of the string. A higher tension and lower mass will result in a higher speed, while a lower tension and higher mass will result in a slower speed.

3. How does the amplitude of a sinusoidal wave change as it travels along a composite string?

The amplitude of a sinusoidal wave remains constant as it travels along a composite string, unless there is interference or damping present. This means that the height of the wave will remain the same as it moves along the string.

4. Can a composite string support multiple sinusoidal waves traveling at once?

Yes, a composite string can support multiple sinusoidal waves traveling at once. These waves can interfere with each other, creating complex wave patterns.

5. What is the relationship between the frequency and wavelength of a sinusoidal wave traveling along a composite string?

The frequency and wavelength of a sinusoidal wave traveling along a composite string are inversely proportional. This means that as the frequency increases, the wavelength decreases, and vice versa.

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