Question

A pipe 30 cm long is open at both ends which harmonic mode of pipe resonates with 1.1kHz source? With resonance with the same source be observed if one end of the pipe is closed,take the speed of sound in air as 330m/s

Answer 1

$$\begin{gathered} Forpipeopenatbothends,resonantfrequencyisgivenby \\ f=\frac{n}{2L}v \\ Forpipeclosedatoneendresonantfequencyisgivenby \\ f=\frac{\left(2m+1\right)}{4L}v \\ resonancewilloccurswhenfrequency,f_{s}willbecomeequaltof \\ {f}_s=1.1kHz=1100Hz \\ Wehave \\ L=30cm=0.3m \\ v=330m{s}^{-1} \\ f=\frac{\left(2m+1\right)}{4\times 0.3}\times 330 \\ f=\frac{\left(2m+1\right)}{4\times 3}\times 3300 \\ f=\frac{\left(2m+1\right)}{4}\times 1100 \\ f=\left(2m+1\right)\times 275Hz \\ Weknowm=0,1,2,3,4 \\ f=275Hz,825Hz,1375Hz,... \\ Therefore \\ {f}_S\cancel{=}fforanym \\ Resonancewillnotoccurinpipeopenatoneend \end{gathered}$$