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JEE Main 201815 AprilMorning ShiftOnline

Exam: JEE Main
Year: 2018
Date: 15 April
Shift: Morning Shift
Mode: Online
Subject: Physics
Chapter: Waves and Sound

JEE Main 2018 · 15 April · Morning Shift · Online · Physics · Waves and Sound

A tuning fork vibrates with frequency 256 ~Hz and gives one best...

A tuning fork vibrates with frequency

256 \mathrm{~Hz}

and gives one best per second with the third normal mode of vibration of an open pipe. What is the length of the pipe? (Speed of sound of air is

340 \mathrm{~ms}^{-1}

)

Options

A(a) $190 \mathrm{~cm}$
B $180 \mathrm{~cm}$
C $220 \mathrm{~cm}$
D $200 \mathrm{~cm}$

Correct answer

D. $200 \mathrm{~cm}$

Step-by-step solution

According to question, tuning fork gives 1 beat/second with (N)

3^{\text{rd }}

normal mode. Therefore, organ pipe will have frequency

(256 \pm 1)

\mathrm{Hz}

. In open organ pipe, frequency

\mathrm{n}=

\frac{

\mathrm{NV}

}{2 \ell}

or,

255=

\frac{3 \times 340}{2 \times \ell}

\Rightarrow \ell=2

\mathrm{~m}=

200

\mathrm{~cm}

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