Will the wavelength decrease when the wave moves from a light string to a heavy

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Homework Help Overview

The discussion revolves around the behavior of wave properties, specifically wavelength, when transitioning from a light string to a heavier string. Participants are exploring the relationship between wave speed, frequency, and wavelength in the context of linear density changes.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants are examining whether the wavelength of a wave changes when moving from a lighter to a heavier string, considering the effects of linear density on wave speed and frequency. Questions about the relationships between these variables are being raised, particularly regarding the implications of constant frequency and tension.

Discussion Status

Some participants have provided insights into the relationships between wave speed, frequency, and wavelength, noting that frequency remains constant despite changes in linear density. There is an ongoing exploration of how these changes affect wavelength, with some participants questioning their understanding of the relevant equations.

Contextual Notes

Participants are navigating through potential misconceptions about wave equations and their units, as well as the implications of mass density on wave properties. The discussion reflects a mix of correct and incorrect interpretations of the relationships involved.

insertnamehere
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hi, i was just wondering if a wave's wavelength will change when it goes from a light string to a heavier one. I think it wouldn't affect it, however I know that velocity will be affected as the linear density will be changed. But am I right, will the wavelength remain unaffected?
 
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You're right that the speed changes. It seems that the essential piece of information that you are missing is this: the frequency does not change.

So since you know that [itex]v_1=\lambda_1f_1[/itex] and [itex]v_2=\lambda_2f_2[/itex], so what can you say about the wavelengths?
 
ok, so that means that although the mass of the string increases, this will have no affect whatsoever on the frequency because since
v= sqrt(T/linear density) and also (wavelength/tension)
and increasing the mass of the string will have no affect on the tension, v increases as the tension remains constant, therefore will the wavelength have to INCREASE in order to compensate the equation? Am i on the right track?
 
insertnamehere said:
v= sqrt(T/linear density) and also (wavelength/tension)

The first part is right, but the second part is not. v does not equal (wavelength/tension). That expression doesn't even have the right units to be a speed.

and increasing the mass of the string will have no affect on the tension, v increases as the tension remains constant, therefore will the wavelength have to INCREASE in order to compensate the equation? Am i on the right track?

The wave speed decreases as you move to the string of higher mass density.
 
oh no, i meant v= (wavelength/PERIOD)
 

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