JEE Main · 2014 · 06 Apr 2014 · Offline · Waves & Sound

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A pipe of length 85 cm is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies lie below 1250 Hz. The velocity of sound in air is

340 m / s

(A)6✓ Correct
(B)4
(C)12
(D)8

Answer: (A)

Solution

A pipe closed at one end supports only the odd harmonics. Its fundamental has

\frac{λ}{4} = L = 0.85

m, so

λ = 3.4

m and

f_{0} = \frac{v}{λ} = \frac{340}{3.4} = 100

Hz. The allowed frequencies are

100, 300, 500, 700, 900, 1100

Hz; the next one,

1300

Hz, sits above the

1250

Hz ceiling. That leaves six natural oscillations below

1250

Hz.

JEE Main · 2014 · 06 Apr 2014 · Offline · Single correct option

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