First slide

Stationary waves

Question

The fundamental frequency of a string stretched with a weight of 4 kg is 256 Hz. The weight required to produce its octave is

Moderate

A

4 kg wt
B

8 kg wt
C

12 kg wt
D

16 kg wt

Solution

$n = \frac{1}{2 l} \sqrt{\frac{T}{m}} \Rightarrow n \propto \sqrt{T}$ For octave, $n^{'} = 2 n$
$\Rightarrow \frac{n^{'}}{n} = \sqrt{\frac{T^{'}}{T}} = 2 \Rightarrow T^{'} = 4 T = 16 kg - wt$

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