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Question
The fundamental frequency of a string is proportional to
Options
inverse of its length
the diameter
the tension
the density.
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Solution
inverse of its length
The relation between wave speed and the length of the string is given by
\[v = \frac{1}{2l}\sqrt{\frac{F}{\mathrm{\mu}}}\]
where
l is the length of the string
F is the tension
μ linear mass density
From the above relation, we can say that the fundamental frequency of a string is proportional to the inverse of the length of the string.
\[v \propto \frac{1}{l}\]
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