Question 451: Waves

Question

If n
1
, n
2
and n
3
are the fundamental  frequencies of three segments into which a string is divided, then the original  fundamental frequency n of the string is given by

Accepted Answer

$$n = {1 \over {2l}}\sqrt {{T \over m}} $$
$$ \Rightarrow n \propto {1 \over l} \Rightarrow nl = constant,\,K$$
$$ 	herefore $$ $${n_1}{l_1} = K,{n_2}{l_2} = K,{n_3}{l_3} = K$$
Also, $$l = {l_1} + {l_2} + {l_3}$$
$$ \Rightarrow {K \over n} = {K \over {{n_1}}} + {K \over {{n_2}}} + {K \over {{n_3}}}$$
$$ \Rightarrow {1 \over n} = {1 \over {{n_1}}} + {1 \over {{n_2}}} + {1 \over {{n_3}}}$$

Answer

$${1 \over n} = {1 \over {{n_1}}} + {1 \over {{n_2}}} + {1 \over {{n_3}}}$$

Answer

$${1 \over {\sqrt n }} = {1 \over {\sqrt {{n_1}} }} + {1 \over {\sqrt {{n_2}} }} + {1 \over {\sqrt {{n_3}} }}$$

Answer

$$\sqrt n  = \sqrt {{n_1}}  + \sqrt {{n_2}}  + \sqrt {{n_3}} $$

Answer

n $$=$$ n
1
+ n
2
+ n
3

Waves

If n 1 , n 2 and n 3 are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency n of the string is given by

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