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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

Hitesh Soni
32 Points
6 years ago
we have got two equations here:
1st eq. is-
l1 + e = v/4f.........(1)
2nd eq.is
l2 + e = 3v/4f........(2)
Apply (2) – (1)
l2 - l1 = 3v/4f – v/4f = 2v/4f = v/2f
delta(l2 - l1) / (l2 - l1) = delta(v) / v
delta(v) = 2f delta(l2 - l1) = 2f(deltal1 + deltal2) …......for maximum error
delta(v) = 2 x 512 x (0.1 + 0.1) = 2 x 512 x 0.2
delta(v) = 204.8 cm/s
Hence (c) is correct.
Rishi Sharma
one year ago
Dear Student,

we have got two equations here:
1steq. is-
l1 + e = v/4f.........(1)
2ndeq.is
l2 + e = 3v/4f........(2)
Apply (2) – (1)
l2-l1=3v/4f – v/4f = 2v/4f = v/2f
delta(l2-l1) / (l2-l1) = delta(v) / v
delta(v) = 2f delta(l2-l1) = 2f(deltal1+ deltal2) …......for maximum error
delta(v) = 2 x 512 x (0.1 + 0.1) = 2 x 512 x 0.2
delta(v) = 204.8 cm/s

Thanks and Regards