A tuning fork with frequency 800 hz produce resonance

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A tuning fork with frequency 800 hz produces resonance in a resonance column tube with upper end open and lower end closed by water surface. Successive resonances are observed at lengths 9.75 cm, 31.25 cm and 52.75 cm. The speed of sound in air is,

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Solution :

For the tube open at one the resoN/Asnce frequencies are nv4l when n is a positive odd interger. If the tuning fork has a frequency v and l1,l2,l3 are the successive lengths of the tube in resoN/Ance with it, we have

nv4l1=v

(n+2)v4l2=v

(n+4)v)4l3=v

giv∈gl3−l2=l2−l1=2v4v=v2v

By the question l_3-l_2=(52.75-31.25)cm=21.50cmandl_2-l_1=(31.25-9.75)m=21.50cm.Thus, v/(2v)=21.50cmor v=2vxx21.50cm=2xx800s^-1xx21.50cm=344ms^-1`

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