Question

In an experiment to measure the speed of sound by a resonating air column, a tuning 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 resonancers are heard at air columns of length $50.7cm$ and $83.9cm$. Which of the following statements is (are) true?

• A. The speed of sound determined from this experiment is $332m{s}^{-1}$
• B. The end correction in this experiment is $0.9cm$
• C. The wavelength of the sound wave is $66.4cm$
• D. The resonance at $50.6cm$ corresponds to the fundamental harmonic

Answer 1

The correct option is A The speed of sound determined from this experiment is $332m{s}^{-1}$

$\begin{array}{c}Let{n}_{1}harmoniciscorrespondingto50.7cmand{n}_{2}harmoniciscorresponding83.9cm.\\ Sincebothonecon\sec utiveharmonics\\ \therefore theirdifference=\frac{\lambda }{2}\\ \therefore \frac{\lambda }{2}=\left(83.9-50.7\right)cm\\ \frac{\lambda }{2}=33.2cm\\ \lambda =66.4cm\\ \therefore \frac{\lambda }{4}=16.6cm\\ lengthcorrespondingtofundamentalemustbecloseto\frac{\lambda }{4}and50.7cm,\\ mustbeandoddmultipleofthislength16.6\times 3=49.8cm.\\ Therefore,50.7is{3}^{rd}harmonic\\ e+50.7=\frac{3\lambda }{4}\\ e=49.8-50.7=-0.9cm\\ speedofsound,v=f\lambda \\ \therefore v=500\times 66.4cm/\sec =332m/s\end{array}$

Hence,

option $\left(A\right)$ is correct answer.