The frequency 'v' of vibration of a streched string depends upon
Answers
Answer:
tension,length and mass per unit length
The expression is
Explanation:
The complete question is:
The frequency of vibration of a stretched string depends upon:
a) Its Length l
b) Its mass per unit length m and
c)The tension T in the string.
Obtain dimensionally an expression for frequency.
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,
Thus is the required equation.
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