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Q.

Fundamental frequencies of air columns in three pipes are f, 2f and 4f respectively. The first two tubes are open tubes and the third tube is closed at one end now the three tubes are joined end to end so as to form a single tube with one end closed. Then fundamental frequency of air column in this composite tube is 

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a

3f8

b

4f13

c

5f8

d

6f13

answer is B.

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Detailed Solution

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f=2V4l1l1=V2f2f=2V4l2l2=V4f

and 4f=1.V4l3l3=V16f

Length of the composite tube, l=l1+l2+l3=1316Vf

f1=V4l=V4×(13V16f)=4f13

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