In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency 512 Hz is used. The length of the air column is varied by changing the level of water in the resonance tube. Two successive resonances are heard at air columns of length 50.7 cm and 83.9 cm. Which of the following statements is (are) true?

Let $n_1$  harmonic is corresponding to 50.7 cm and $n_2$  harmonic is corresponding to 83.9 cm  since both are consecutive harmonics. The difference in the lengths of air columns of two  resonances should be  $\frac{\lambda }{2}$
 
$\therefore \frac{\lambda }{2}=(83.9-50.7)CM$  
Or     $\frac{\lambda }{2}=33.2cm$
Hence   $\lambda =66.4cm$
Hence option (3) is correct. 
Hence the length corresponding to fundamental mode must be close to $\frac{\lambda }{4}$.
 $\therefore \frac{\lambda }{4}=16.6cm$ 
It means the length 50.7 cm must be an odd multiple of this length $16.6\times 3=49.8cm$. Therefore 50.7 is 3rd harmonic. 
If end correction is $e$, then  $e+50.7=\frac{3\lambda }{4}$
 $e=49.8-50.7=-0.9cm$
Hence option (2) is correct. 
Speed of sound,  $v=f\lambda$
$\therefore v=500\times 66.4cm/\sec =332m/s$  
Hence option (1) is correct