A-pipe-closed-at-one-end-emits-sound-wave-of-frequency-440-Hz-i-Determine-the-length-of-the-air-column-ii-Frequencies-of-the-second-harmonic-and-the-third-harmonic-Velocity-of-sound-is-330m-s-Re

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Question Number 10728 by Saham last updated on 23/Feb/17

$$\mathrm{A}\mathrm{pipe}\mathrm{closed}\mathrm{at}\mathrm{one}\mathrm{end}\mathrm{emits}\mathrm{sound}\mathrm{wave}\mathrm{of}\mathrm{frequency}440\mathrm{Hz}.$$$$\left(\mathrm{i}\right)\mathrm{Determine}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{air}\mathrm{column}$$$$\left(\mathrm{ii}\right)\mathrm{Frequencies}\mathrm{of}\mathrm{the}\mathrm{second}\mathrm{harmonic}\mathrm{and}\mathrm{the}\mathrm{third}\mathrm{harmonic}$$$$\mathrm{Velocity}\mathrm{of}\mathrm{sound}\mathrm{is}330\mathrm{m}/\mathrm{s}$$$$\mathrm{Refractive}\mathrm{index}\mathrm{of}\mathrm{glass}\mathrm{is}1.50,\mathrm{that}\mathrm{of}\mathrm{air}\mathrm{is}1.00,$$$$\mathrm{and}\mathrm{that}\mathrm{of}\mathrm{water}\mathrm{is}1.33$$

Answered by sandy_suhendra last updated on 23/Feb/17

$$\left(\mathrm{i}\right){\mathrm{f}}_1=440\mathrm{Hz}$$$$\mathrm{v}={\mathrm{f}}_1.{\lambda }_1\Rightarrow {\lambda }_1=\frac{\mathrm{v}}{{\mathrm{f}}_1}=\frac{330}{440}=0.75\mathrm{m}$$$$\mathrm{the}\mathrm{air}\mathrm{column}={\mathrm{h}}_1=\frac{1}{4}{\lambda }_1=\frac{1}{4}\times 0.75=0.1875\mathrm{m}$$$$\left(\mathrm{ii}\right){\mathrm{f}}_1:{\mathrm{f}}_2:{\mathrm{f}}_3:\dots =1:3:5:\dots$$$$\mathrm{second}\mathrm{harmonic}={\mathrm{f}}_2=\frac{3}{1}\times 440=1,320\mathrm{Hz}$$$$\mathrm{third}\mathrm{harmonic}={\mathrm{f}}_3=\frac{5}{1}\times 440=2,200\mathrm{Hz}$$

Commented by Saham last updated on 23/Feb/17

$$\mathrm{Thanks}\mathrm{for}\mathrm{your}\mathrm{help}.\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$

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