Finding Velocity of Traverse Wave on String Using Dimensional Analysis

In summary, the velocity of a traverse wave traveling along a string can be found using dimensional analysis by setting it equal to the tension of the string (F) raised to an exponent (x) and its mass per length unit (u) raised to another exponent (y). The units for mass per length are typically kg/m.
  • #1
pinsickle
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Homework Statement


The velocity of a traverse wave traveling along a string depends on the tension of the string, F, which has units of force, and its mass per length unit u.
Assume v = F^x * u^y. The values may be found using dimensional analysis.


Homework Equations


I am pretty sure I understand dimensional analysis. I just don't know what the units are for "mass per length" . I am assuming that the Force is in Newtons (kg * m /s^2) and I know velocity is (m/s). Sorry for the goofy question but I'm still waiting on my book to come in from Amazon and I can't to find an answer on Google for mass per length. Thanks


The Attempt at a Solution


I don't want help with solving the problem itself. I am just wondering what mass per unit length means so I can solve the question.
 
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  • #2
Nevermind I just figured out it is kg/m
 
  • #3
pinsickle said:
Nevermind I just figured out it is kg/m

They are distinguishing between "units" and "dimensions" -- for example, velocity has dimensions length/time no matter what system of units you use. But yes, it's easier just to put the units in.
 

What is dimensional analysis?

Dimensional analysis is a mathematical method used to check the correctness of an equation or to derive a relationship between physical quantities. It involves analyzing the dimensions of various physical quantities involved in a problem to determine the relation between them.

How is dimensional analysis used to find the velocity of a traverse wave on a string?

Dimensional analysis can be used to find the velocity of a traverse wave on a string by considering the physical quantities involved in the problem, such as the tension of the string, the wavelength, and the frequency. By analyzing the dimensions of these quantities, an equation can be derived to calculate the velocity of the wave.

What are the dimensions of velocity?

The dimensions of velocity are length per unit time, represented as [L/T]. This means that velocity is a physical quantity that has both a magnitude (length) and a direction, and it is measured in units of length per unit time, such as meters per second or kilometers per hour.

How does the tension of the string affect the velocity of the wave?

The tension of the string has a direct impact on the velocity of the wave. As the tension increases, the velocity of the wave also increases, and vice versa. This is because the tension of the string affects the frequency of the wave, which is one of the factors in the equation for the velocity of the wave.

Can dimensional analysis be used to find the velocity of other types of waves?

Yes, dimensional analysis can be used to find the velocity of other types of waves, such as longitudinal waves or surface waves. The method is the same – analyzing the dimensions of the physical quantities involved in the problem to derive an equation for the velocity of the wave.

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