Question 524: Waves

Question

If the tension and diameter of a sonometer wire of fundamental frequency n is doubled and density is halved then its fundamental frequency will become

Accepted Answer

$$n = {1 \over {2l}}\sqrt {{T \over {\pi {r^2}\rho }}} $$
$$\rho _1^{'} = {\rho  \over 2};T' = 2T$$
D' = 2D or r' = 2r
$$n' = {1 \over {2l}}\sqrt {{{2T} \over {\pi {{\left( {2r} \right)}^2}{\rho  \over 2}}}} $$
After solving, $$n' = {1 \over {2l}}\sqrt {{{2T} \over {\pi {r^2}l}}}  = n$$

Answer

$${\pi  \over 4}$$

Answer

$$\sqrt 2 n$$

Answer

n

Answer

$${n \over {\sqrt 2 }}$$

Waves

If the tension and diameter of a sonometer wire of fundamental frequency n is doubled and density is halved then its fundamental frequency will become

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