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14.Waves and Sound
medium
The length, tension, diameter and density of a wire $B$ are double than the corresponding quantities for another stretched wire $A$. Then.
A
The fundamental frequency of $A$ is equal to the third overtone of $B$
B
The velocity of wave in $B$ is $\frac{1}{{\sqrt 2 }}$ times that of $A$. times that of velocity in $A.$
C
The velocity of wave in $B$ is half that of velocity in $A$
D
both $(A)$ and $(c)$
Solution
We know,
$v =\sqrt{\frac{T}{\mu}}$
Also, $\mu \propto r^2$
Thus,
$v_A \propto \sqrt{\frac{T}{\rho(r)^2}}$
$v_B \propto \sqrt{\frac{2 T}{2 p(2 r)^2}}$
$v_B=\frac{v_A}{2}$
Also,
$n _{ S }=\frac{1}{2(2 L )} \sqrt{\frac{2 T }{8 \mu}}$
$n _{ S }=\frac{1}{8 L } \sqrt{\frac{ T }{\mu}}$
$n _{ A }=4 n _{ B }$
Standard 11
Physics
