Wave Motion Theory Part4

CBSE Physics/ Lakshmikanta Satapathy/ Wave motion/ Vibration of air columns/ Open & closed pipes/ Fundamental frequency & overtones/ End correction/ Resonance tube

1. © Physics Helpline Physics Helpline L K Satapathy Wave Motion Theory-4 Vibration of Air Columns Open & Closed Pipes Fundamental frequency & Overtones End Correction Resonance Tube

2. © Physics Helpline Physics Helpline L K Satapathy Wave Motion Theory-4 Vibration of air columns in closed pipes : Consider an air column trapped in a pipe of length L , closed at one end. The open end is always an antinode and the closed end is always a node. Fundamental mode : In this mode , there is no node between the node and antinode at the ends. Let the wavelength frequency L From the fig. we have  Fundamental frequency is Speed of sound 1 loop =  / 2

3. © Physics Helpline Physics Helpline L K Satapathy Wave Motion Theory-4 First overtone : In this mode , there is one node between the node and antinode at the ends. Let the wavelength frequency From the fig. we have  Frequency of 1 st overtone is  1 st overtone = 3 rd Harmonic Speed of sound

4. © Physics Helpline Physics Helpline L K Satapathy Wave Motion Theory-4 Second overtone : In this mode , there are two nodes between the node and antinode at the ends. Let the wavelength frequency From the fig. we have  Frequency of 2 nd overtone is  2 nd overtone = 5 th Harmonic  In general (n) th overtone = (2n+1) th Harmonic Frequencies obtained in a closed pipe are : [ Odd harmonics ] Speed of sound

5. © Physics Helpline Physics Helpline L K Satapathy Wave Motion Theory-4 Vibration of air columns in open pipes : Consider an air column trapped in a pipe of length L , open at both ends. Hence antinodes are formed at the two open ends. Fundamental mode : In this mode , there is one node between the two antinodes at the ends. Let the wavelength frequency From the fig. we have  Fundamental frequency is L Speed of sound

6. © Physics Helpline Physics Helpline L K Satapathy Wave Motion Theory-4 First overtone : In this mode , there are two nodes between the two antinodes at the ends. Let the wavelength frequency From the fig. we have  Frequency of 1 st overtone is  1 st overtone = 2 nd Harmonic Speed of sound

7. © Physics Helpline Physics Helpline L K Satapathy Wave Motion Theory-4 Second overtone : In this mode , there are three nodes between the two antinodes at the ends. Let the wavelength frequency From the fig. we have  Frequency of 2 nd overtone is  2 nd overtone = 3 rd Harmonic  In general (n) th overtone = (n+1) th Harmonic Frequencies obtained in an open pipe are : [ All harmonics ] Speed of sound

8. © Physics Helpline Physics Helpline L K Satapathy Wave Motion Theory-4 End correction : It is observed that the antinode formed at an open end is not formed exactly at the open end but at a small distance ( e ) outside the open end. The end correction ( e ) depends on the diameter (d) of the pipe as e = 0.3 d This correction is to be applied at each open end of the pipe Effective length = L + e For a closed pipe of length L For an open pipe of length L Effective length = L + 2 e L L

9. © Physics Helpline Physics Helpline L K Satapathy Wave Motion Theory-4 Speed of sound in air [ Resonance tube ] The length of air column in a pipe can be adjusted by controlling the water level in it. The air column is made to vibrate in resonance with an excited tuning fork kept over the mouth of the pipe. Let us keep an excited tuning fork of frequency f at the mouth of the tube and gradually decrease the level of water in the tube from top. 1 st and 2 nd resonances occur at lengths : Let wavelength =  and speed of sound = v

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