Wave motionMediumBloom L3
Question
What is the fractional change in the tension necessary in a sonometer of fixed length to produce a note one octave lower (half of original frequency) than before
Options
A.1/4
B.1/2
C.2/3
D.3/4
Solution
Sol. $f = \frac{nv}{2L}$ length fixed. v∝$\sqrt{T}$
$f \propto \sqrt{T}$
$f' = \frac{f}{2}$
$\frac{f}{\sqrt{T}} = \frac{f'}{\sqrt{T'}}$
$T' = \frac{T}{4}$
Fractional change$= \frac{\Delta T}{T} = \frac{T - T/4}{T} = \frac{3}{4}$
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