Question

unswers
A string is divided into three segments, so that the
segments have fundamental frequencies in the ratio
1:2:3. The length of three segments are in the
ratio​

Answer 1

Answer:

Ratio of the length of three segments is given as

$L_1 : L_2 : L_3 = 1 : \frac{1}{2} : \frac{1}{3}$

Explanation:

As we know that fundamental frequency is given by the formula

$f_o = \frac{1}{2L}\sqrt{\frac{T}{\mu}}$

now we know that ratio of frequency in the string is

$f_1 : f_2 : f_3 = 1 : 2 : 3$

now by above formula we know that

$\frac{1}{2L_1}\sqrt{\frac{T}{\mu}} : \frac{1}{2L_2}\sqrt{\frac{T}{\mu}} : \frac{1}{2L_3}\sqrt{\frac{T}{\mu}} = 1 : 2 : 3$

so we will have

$L_1 : L_2 : L_3 = 1 : \frac{1}{2} : \frac{1}{3}$

#Learn

Topic : Standing waves

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