An air column in tun=be 32cm long, closed at one end, is in resonace with a tuning fork. The air column in another tube, open at both ends, of length 66cm is in resonance with another tuning frok.When those two tuning forks are sounded together , they produce 8 beats per second together, they produce 8 beats per second. then the frquencies of the twpo tuning forks are, (consider fundamental frequencies only)

Options

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

Answer

C

Explanation

The frequency of closed end of column is `V_1=V/4l_1`
The frequency of an open end of column is `V_2=V/2l_1`
`v_(beat)=v_1-v_2`
`8=v/(4xx32)-v/(2xx66)`
`8=v/(128)-v/(132)`
`implies v=8448xx4=33792`
`:. v_1=33792/128=264 "Hz"`
` v_2=33792/132=256 "Hz"`