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Solution - Calculate the Ratio of Lengths of Their Air Columns - Study of Vibrations of Air Columns

Question

The fundamental frequency of an air column in a pipe closed at one end is in unison with the third overtone of an open pipe. Calculate the ratio of lengths of their air columns

Solution

Given that n3 = no
where n3 = frequency of the third overtone of the open pipe
no = fundamental frequency of the closed pipe

Third overtone of open pipe is

`n_3=4(V/(2L_3))`

Fundamental frequency of closed pipe at one end is

`n_o=V/(4L_o)`

`V/(4L_o)=4(V/(2L_3)) `..........(∵ no=n3)

`thereforeL_o/L_3=1/8`

`therefore L_0:L_3=1:8`

Is there an error in this question or solution?

APPEARS IN

2015-2016 (March)
Question 1.6 | 2 marks
Solution for question: Calculate the Ratio of Lengths of Their Air Columns concept: Study of Vibrations of Air Columns. For the courses HSC Science (Computer Science), HSC Science (Electronics), HSC Science (General)
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