General Physics> In a resonance tube with tuning fork of f...

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

Tulika Sureka , 10 Years ago

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2 Answers

Hitesh Soni

Last Activity: 10 Years ago

we have got two equations here:

1^st eq. is-

l₁ + e = v/4f.........(1)

2^nd 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

Last Activity: 4 Years ago

Dear Student,
Please find below the solution to your problem.

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