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In a resonance tube with tuning fork of frequency 512Hz, first resonance occurs at water level equal to 30.3 cm and second resonance occurs at 63.7 cm. The maximum possible error in the speed of sound is (A) 51.2 cm/s (B) 102.4 cm/s (C) 204.8 cm/s (D) 153.6 cm/s
we have got two equations here:1st eq. is-l1 + e = v/4f.........(1)2nd eq.isl2 + e = 3v/4f........(2)Apply (2) – (1)l2 - l1 = 3v/4f – v/4f = 2v/4f = v/2fdelta(l2 - l1) / (l2 - l1) = delta(v) / vdelta(v) = 2f delta(l2 - l1) = 2f(deltal1 + deltal2) …......for maximum errordelta(v) = 2 x 512 x (0.1 + 0.1) = 2 x 512 x 0.2delta(v) = 204.8 cm/sHence (c) is correct.
Dear Student,Please find below the solution to your problem.we have got two equations here:1steq. is-l1 + e = v/4f.........(1)2ndeq.isl2 + e = 3v/4f........(2)Apply (2) – (1)l2-l1=3v/4f – v/4f = 2v/4f = v/2fdelta(l2-l1) / (l2-l1) = delta(v) / vdelta(v) = 2f delta(l2-l1) = 2f(deltal1+ deltal2) …......for maximum errordelta(v) = 2 x 512 x (0.1 + 0.1) = 2 x 512 x 0.2delta(v) = 204.8 cm/sThanks and Regards
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