Question

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 :

• A. $500$
• B. $300$
• C. $330$
• D. $165$

Answer 1

The correct option is A $500$

Let the resonance column has the end correction to be $x$.

Length of the air column for first resonance to occur $l_1=16cm=0.16$ $m$

Using for Ist resonance $l_1+x=\frac{\lambda }{4}$

Length of the air column for second resonance to occur $l_2=49cm=0.49$ $m$

For second resonance $l_2+x=\frac{3\lambda }{4}$

$⟹$ $l_2-l_1=\frac{\lambda }{2}$

$\therefore$ $0.49-0.16=\frac{\lambda }{2}$ $⟹\lambda =0.66$ m

From $v=\nu \lambda$, we get $330=\nu \times 0.66$

$⟹$ $\nu =500$ $Hz$