Question

An air column in a tube $32cm$ long, closed at one end, is in resonance with a tuning fork. The air column in another tube, open at both ends, of length $66cm$ is in resonance with another tuning fork. When these two tuning forks are sounded together, they produce $8$ beats per second. Then the frequencies of the two tuning forks are:
(Consider fundamental frequencies only)

• A. $250Hz,258Hz$
• B. $240Hz,248Hz$
• C. $264Hz,256Hz$
• D. $280Hz,272Hz$

Answer 1

The correct option is C $264Hz,256Hz$

Since $v=n\lambda$ and velocity in two cases must be same as the medium is same. ${\lambda }_1=4\left(32\right)cm=128cm$ and ${\lambda }_2=2\left(66\right)cm=132cm$.

Hence, $\frac{n_1}{n_2}=\frac{{\lambda }_2}{{\lambda }_1}=\frac{132}{128}=\frac{33}{32}$.

Also, $n_1-n_2=8$,

Solving these gives $n_1=264Hz$ and $n_1=256Hz$.