Discussion Forum

In an experiment to measure the speed of sound by a resonating air column, a turning fork of frequency 500Hz 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  50.7cm and 83.9 cm . Which of the following statements is (are) true?

Answer:

Explanation:

Let n th harmonic is  corresponding to 50.7 cm and (n+1)th harmonic is corresponding 83.9 cm.

               Their difference is $\frac{\lambda}{2}$

   $\frac{\lambda}{2}$   = (83.9 - 50.7) cm

                     $\lambda$    = 66.4 cm

  $\frac{\lambda}{4}$     = 16.6 cm

   Length corresponding to fundamental mode must be close to   $\frac{\lambda}{4}$ and 50.7 cm must be an odd multiple  of this length 16.6 × 3 =49.8 cm. Therefore, 50.7 is 3rd  harmonic.

   If end correction is e, then

           $e+50.7=\frac{3\lambda}{4}$

      e= 49.8 - 50.7 = -.09 cm

          speed of sound  ,  $v=f\lambda$

 v= 500 × 66.4 cm/s   =332 m/s