First slide

Sonometer

Question

What is the percentage change in the tension necessary in a sonometer of fixed length to produce a note one octave lower (half of original frequency) than before?

Easy

A

25%
B

50%
C

67%
D

75%

Solution

In Sonometer $V \propto \sqrt{T}$
$∴ \frac{V_{1}}{V_{2}} = 2 = \sqrt{\frac{T_{1}}{T_{2}}} \Rightarrow T_{2} = \frac{T_{1}}{4}$
$\frac{T_{1} - T_{2}}{T_{1}} \times 100 = \frac{T_{1} - \frac{T_{1}}{4}}{T_{1}} \times 100 = 75 %$

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