Question and Answers Forum

All Questions      Topic List

Others Questions

Previous in All Question      Next in All Question      

Previous in Others      Next in Others      

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

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 Refractive index of glass is 1.50, that of air is 1.00, and that of water is 1.33

$$\mathrm{A}\:\mathrm{pipe}\:\mathrm{closed}\:\mathrm{at}\:\mathrm{one}\:\mathrm{end}\:\mathrm{emits}\:\mathrm{sound}\:\mathrm{wave}\:\mathrm{of}\:\mathrm{frequency}\:\mathrm{440}\:\mathrm{Hz}.\: \\ $$$$\left(\mathrm{i}\right)\:\mathrm{Determine}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{air}\:\mathrm{column} \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{Frequencies}\:\mathrm{of}\:\mathrm{the}\:\mathrm{second}\:\mathrm{harmonic}\:\mathrm{and}\:\mathrm{the}\:\mathrm{third}\:\mathrm{harmonic} \\ $$$$\mathrm{Velocity}\:\mathrm{of}\:\mathrm{sound}\:\mathrm{is}\:\mathrm{330m}/\mathrm{s} \\ $$$$\mathrm{Refractive}\:\mathrm{index}\:\mathrm{of}\:\mathrm{glass}\:\mathrm{is}\:\mathrm{1}.\mathrm{50},\:\mathrm{that}\:\mathrm{of}\:\:\mathrm{air}\:\mathrm{is}\:\mathrm{1}.\mathrm{00},\: \\ $$$$\mathrm{and}\:\mathrm{that}\:\mathrm{of}\:\mathrm{water}\:\mathrm{is}\:\mathrm{1}.\mathrm{33} \\ $$

Answered by sandy_suhendra last updated on 23/Feb/17

(i) f_1 =440 Hz v=f_1 .λ_1 ⇒ λ_1 =(v/f_1 )=((330)/(440))=0.75 m the air column=h_1 =(1/4)λ_1 =(1/4)×0.75=0.1875 m (ii) f_1 : f_2 : f_3 : ... = 1 : 3 : 5 : ... second harmonic=f_2 =(3/1)×440=1,320 Hz third harmonic=f_3 =(5/1)×440=2,200 Hz

$$\left(\mathrm{i}\right)\:\mathrm{f}_{\mathrm{1}} =\mathrm{440}\:\mathrm{Hz} \\ $$$$\mathrm{v}=\mathrm{f}_{\mathrm{1}} .\lambda_{\mathrm{1}} \:\Rightarrow\:\lambda_{\mathrm{1}} =\frac{\mathrm{v}}{\mathrm{f}_{\mathrm{1}} }=\frac{\mathrm{330}}{\mathrm{440}}=\mathrm{0}.\mathrm{75}\:\mathrm{m}\:\:\: \\ $$$$\mathrm{the}\:\mathrm{air}\:\mathrm{column}=\mathrm{h}_{\mathrm{1}} =\frac{\mathrm{1}}{\mathrm{4}}\lambda_{\mathrm{1}} =\frac{\mathrm{1}}{\mathrm{4}}×\mathrm{0}.\mathrm{75}=\mathrm{0}.\mathrm{1875}\:\mathrm{m}\:\:\: \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{f}_{\mathrm{1}} \::\:\mathrm{f}_{\mathrm{2}} \::\:\mathrm{f}_{\mathrm{3}} \::\:...\:=\:\mathrm{1}\::\:\mathrm{3}\::\:\mathrm{5}\::\:... \\ $$$$\mathrm{second}\:\mathrm{harmonic}=\mathrm{f}_{\mathrm{2}} =\frac{\mathrm{3}}{\mathrm{1}}×\mathrm{440}=\mathrm{1},\mathrm{320}\:\mathrm{Hz} \\ $$$$\mathrm{third}\:\mathrm{harmonic}=\mathrm{f}_{\mathrm{3}} =\frac{\mathrm{5}}{\mathrm{1}}×\mathrm{440}=\mathrm{2},\mathrm{200}\:\mathrm{Hz} \\ $$

Commented by Saham last updated on 23/Feb/17

Thanks for your help. God bless you sir.

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

Terms of Service

Privacy Policy

Contact: info@tinkutara.com