Discussion Forum



1)

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?


A) The speed of sound determined from this experiment is $332 ms^{-1}$

B) The end correction in this experiment is 0.9 cm

C) The wavelength of the sound wave is 66.4 cm

D) The resonance at 50.7 cm corresponds to the fundamental harmonic

Answer:

Option A,C

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