Question 461: Waves

Question

When a string is divided into three segments of length $$l$$
1
, $$l$$
2
and $$l$$
3
the fundamental frequencies of these three segments are $${\upsilon _1},{\upsilon _2}$$ and $${\upsilon _3}$$ respectively. The original fundamental frequency ($$v$$) of the string is

Accepted Answer

Let $$l$$ be the length of the string. Fundamental frequency is given by
$$\upsilon  = {1 \over {2l}}\sqrt {{T \over \mu }} $$
$$ \Rightarrow v \propto {1 \over l}$$  ($$ \because $$ T and $$\mu $$ are constants)
Here, $${l_1} = {k \over {{\upsilon _1}}},{l_2} = {k \over {{\upsilon _2}}},{l_3} = {k \over {{\upsilon _3}}}$$ and $$ l = {k \over \upsilon }$$
But  $$l = l_1 + l_2 + l_3$$
$${1 \over \upsilon } = {1 \over {{\upsilon _1}}} + {1 \over {{\upsilon _2}}} + {1 \over {{\upsilon _3}}}$$

Answer

$$\sqrt v  = \sqrt {{v_1}}  + \sqrt {{v_2}}  + \sqrt {{v_3}} $$

Answer

$$v = {v_1} + {v_2} + {v_3}$$

Answer

$${1 \over v} = {1 \over {{v_1}}} + {1 \over {{v_2}}} + {1 \over {{v_3}}}$$

Answer

$${1 \over {\sqrt v }} = {1 \over {\sqrt {{v_1}} }} + {1 \over {\sqrt {{v_2}} }} + {1 \over {\sqrt {{v_3}} }}$$

Waves

When a string is divided into three segments of length $l 1 , l 2 and l 3 the fundamental frequencies of these three segments are {\upsilon _1},{\upsilon _2} and {\upsilon _3} respectively. The original fundamental frequency (v$) of the string is

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