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Reflection from a Fixed End

A weight of 5...

Question

A weight of 5 kg is required to produce the fundamental frequency of a sonometer wire. What weight is required to produce its octave?

A

20

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B

32

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C

26

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D

none of the above

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Solution

The correct option is C 20
In a sonometer wire,
$f \propto \sqrt{T}$
$f_{o c t a v e} = 2 f_{f u n d a m e n t a l}$
$T_{o c t a v e} = 4 T_{f u n d a m e n t a l}$
$M_{o c t a v e} g = 4 m_{f u n d a m e n t a l}$
$M_{o c t a v e} = 20 k g$

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