How to maintain the same stationary wave pattern?

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Homework Help Overview

The discussion revolves around maintaining a stationary wave pattern on a string, focusing on the relationship between wave speed, frequency, and wavelength. Participants are exploring how changes in these parameters affect the formation of standing waves.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the relationship between wave speed, frequency, and wavelength, particularly in the context of maintaining a stationary wave pattern. There is confusion regarding the correct approach to adjusting wave speed and the implications of changing frequency.

Discussion Status

Some participants have offered insights into the conditions required for standing waves, such as the necessity for the string length to be a half-integer multiple of the wavelength. Others have suggested looking into the wave equation for further understanding of wave velocity in relation to string tension and density.

Contextual Notes

There is an acknowledgment that the wavelength of a stationary wave cannot be easily changed, which raises questions about how to adjust wave speed effectively. Participants are also considering the implications of changing frequency on the overall wave behavior.

toforfiltum
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Homework Statement


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Homework Equations


not sure

The Attempt at a Solution


The answer is C, though I answered B. I don't understand why C is the answer.I thought that to maintain the same stationary wave pattern, I must maintain the speed of the stationary wave, and one way to do this is by reducing the wavelength of the wave. Instead, the answer suggests that we increase the speed of wave instead. Is it done to match the increase in frequency? But even so, why is B wrong?
 
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In order to have a standing wave, the string length needs to be a half-integer multiple of the wavelength. You therefore cannot change the wavelength. How would you achieve this when the frequency changes? (Hint: How does frequency relate to wave speed?)
 
Orodruin said:
In order to have a standing wave, the string length needs to be a half-integer multiple of the wavelength. You therefore cannot change the wavelength. How would you achieve this when the frequency changes? (Hint: How does frequency relate to wave speed?)
Ah, I forgot the fact that the wavelength of a stationary wave cannot be simply changed. Anyway, how do you increase the speed of wave on the string?
 
toforfiltum said:
Ah, I forgot the fact that the wavelength of a stationary wave cannot be simply changed. Anyway, how do you increase the speed of wave on the string?

Have you seen the derivation of the wave equation for a string? If not you should look it up, it will tell you the wave velocity in terms of the density and string tension. Changing either will change the wave velocity.
 
Orodruin said:
Have you seen the derivation of the wave equation for a string? If not you should look it up, it will tell you the wave velocity in terms of the density and string tension. Changing either will change the wave velocity.
Ok, thanks.
 

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