In a resonance tube the first resonance with a tuning fork occurs at 16 cm and second at 49 cm. If the velocity of sound is 330 m/s, the frequency of tuning fork is

(1) 500

(2) 300

(3) 330

(4) 165

(1) For closed pipe ${l}_{1}=\frac{v}{4n}$;

${l}_{2}=\frac{3v}{4n}$$v=2n\text{\hspace{0.17em}}\left({l}_{2}-{l}_{1}\right)$

$n=\frac{v}{2\left({l}_{2}-{l}_{1}\right)}=\frac{330}{2×\left(0.49-0.16\right)}=500\text{\hspace{0.17em}}Hz$

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