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Question
A wire of length 2⋅00 m is stretched to a tension of 160 N. If the fundamental frequency of vibration is 100 Hz, find its linear mass density.
Solution
Given:
Length of the wire (L)= 2.00 m
\tect{ Fundamental frequency }of the vibration (f0) = 100 Hz
Applied tension (T) = 160 N
\[Fundamental frequency, f_0 = \frac{1}{2L}\sqrt{\left( \frac{T}{m} \right)}\]
\[ \Rightarrow 10 = \frac{1}{4}\sqrt{\frac{160}{m}}\]
\[ \Rightarrow m = 1 \times {10}^{- 3} kg/m\]
\[ \Rightarrow m = 1 g/m\]
So, the linear mass density of the wire is 1 g/m.
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