Derive the equation of frequency of vibration of string that depends upon its length its mass per unit area
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Explanation:
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The equation is
Explanation:
Let the frequency of vibration v depends upon, length l, tension T and mass per unit length m in the following way
, where k is a constant
Dimensions of v = [T⁻¹]
Dimensions of l = [L]
Dimensions of T = [MLT⁻²]
Dimensions of m = [ML⁻¹]
Thus,
LHS Dimensions =RHS Dimensions
Comparing the dimensions on both sides
We get
............. (1)
..............(2)
................... (3)
From eq (3)
Thus, from eq (1)
And from eq (2)
Thus, the equation becomes
or,
or,
This is the required equation.
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