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

In summary, the wavelength of a wave will not change when it goes from a lighter string to a heavier one. However, the velocity will be affected due to the change in linear density. The frequency of the wave remains constant. The relationship between wave speed, wavelength, and tension is v = sqrt(T/linear density), not (wavelength/tension). Increasing the mass of the string will not affect the tension, but it will decrease the wave speed. The correct equation is v = wavelength/period.
  • #1
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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  • #2
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?
 
  • #3
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?
 
  • #4
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.
 
  • #5
oh no, i meant v= (wavelength/PERIOD)
 

1. Will the wavelength always decrease when a wave moves from a light string to a heavy string?

No, the wavelength may either increase or decrease depending on the properties of the two strings, such as their tension and density.

2. How does the wavelength change when a wave moves from a light string to a heavy string?

The wavelength changes because the speed of the wave is affected by the properties of the string. In general, a heavier string will have a higher wave speed, leading to a shorter wavelength.

3. What other factors besides the weight of the string can affect the wavelength of a wave?

The tension of the string, the density of the medium through which the wave is traveling, and the frequency of the wave can also affect the wavelength.

4. Is there a specific mathematical relationship between the wavelength and the properties of the string?

Yes, the wavelength is inversely proportional to the square root of the tension and directly proportional to the square root of the density of the string. This relationship is described by the wave equation.

5. Can the wavelength of a wave be controlled by changing the properties of the string?

Yes, by adjusting the tension and/or density of the string, one can control the speed of the wave and therefore the wavelength. This is how musical instruments, such as guitars and violins, produce different pitches.

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