String Oscillations
المؤلف:
Sidney B. Cahn Boris E. Nadgorny
المصدر:
A GUIDE TO PHYSICS PROBLEMS
الجزء والصفحة:
part 1 , p 9
2-8-2016
1225
String Oscillations
The frequency of oscillation of a string depends on its length L, the force applied to its ends T, and the linear mass density ρ. Using dimensional analysis, find this dependence.
SOLUTION
We have assumed that the dependence is of the form
To find α, β, γ we use dimensional analysis, i.e., assume that the dimensions are equivalent on both sides of our proportion:
In MKS units, we have
Or
This is true if the following equations hold:
So
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